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1.
A. A. Ivanov 《Communications in Mathematical Physics》2011,307(1):1-16
The Majorana representations of groups were introduced in Ivanov (The Monster Group and Majorana Involutions, 2009) by axiomatising some properties of the 2A-axial vectors of the 196 884-dimensional Monster algebra, inspired by the sensational classification of such representations
for the dihedral groups achieved by Sakuma (Int Math Res Notes, 2007). This classification took place in the heart of the theory of Vertex Operator Algebras and expanded earlier results by Miyamoto
(J Alg 268:653–671, 2003). Every subgroup G of the Monster which is generated by its intersection with the conjugacy class of 2A-involutions possesses the (possibly unfaithful) Majorana representation obtained by restricting to G the action of the Monster on its algebra. This representation of G is said to be based on an embedding of G in the Monster. So far the Majorana representations have been classified for the groups G isomorphic to the symmetric group S
4 of degree 4 (Ivanov et al. in J Alg 324:2432–2463, 2010), the alternating group A
5 of degree 5 (Ivanov AA, Seress á in Majorana Representations of A
5, 2010), and the general linear group GL
3(2) in dimension 3 over the field of two elements (Ivanov AA, Shpectorov S in Majorana Representations of L
3(2), 2010). All these representations are based on embeddings in the Monster of either the group G itself or of its direct product with a cyclic group of order 2. The dimensions and shapes of these representations are given
in the following table: 相似文献
2.
Spatial noncommutativity is similar and can even be related to the non- Abelian nature of multiple D-branes. But they have
so far seemed independent of each other. Reflecting this decoupling, the algebra of matrix valued fields on noncommutative
space is thought to be the simple tensor product of constant matrix algebra and the Moyal-Weyl deformation. We propose scenarios
in which the two become intertwined and inseparable. Therefore the usual separation of ordinary or noncommutative space from
the internal discrete space responsible for non-Abelian symmetry is really the exceptional case of an unified structure. We
call it non-Abelian geometry. This general structure emerges when multiple D-branes are configured suitably in a flat but varying B field background, or in the presence of non-Abelian gauge field background. It can also occur in connection with Taub-NUT
geometry. We compute the deformed product of matrix valued functions using the lattice string quantum mechanical model developed
earlier. The result is a new type of associative algebra defining non-Abelian geometry. A possible supergravity dual is also
discussed.
Received: 13 December 2000 / Accepted: 24 October 2002 Published online: 24 January 2003
Communicated by R. H. Dijkgraaf 相似文献
3.
We present a general method for the computation of tree-level superpotentials for the world-volume theory of B-type D-branes.
This includes quiver gauge theories in the case that the D-brane is marginally stable. The technique involves analyzing the
A∞-structure inherent in the derived category of coherent sheaves. This effectively gives a practical method of computing correlation
functions in holomorphic Chern–Simons theory. As an example, we give a more rigorous proof of previous results concerning
3-branes on certain singularities including conifolds. We also provide a new example. 相似文献
4.
Michael P. Tuite 《Communications in Mathematical Physics》1992,146(2):277-309
We consider the Monster Module of Frenkel, Lepowsky, and Meurman as aZ
2 orbifold of a bosonic string compactified by the Leech lattice. We show that the main Conway and Norton Monstrous Moonshine properties, stating that the Thompson series for each Monster group conjugacy class has a modular invariance group of genus zero, follow from an orbifold construction based on an orbifold group composed of Monster group elements. it is shown that a conjectured vacuum structure for the orbifold twisted sectors is sufficient to specify the modular group and the genus zero property for each Thompson series. It is also shown that the Power Map formula of Conway and Norton follows from the same vacuum structure. Finally, we demonstrate the validity of the vacuum conjectures for sectors twisted by Leech lattice automorphisms in many cases. 相似文献
5.
6.
Continuous-wave tunable Cr2+:ZnS laser 总被引:1,自引:0,他引:1
I.T. Sorokina E. Sorokin S. Mirov V. Fedorov V. Badikov V. Panyutin A. Di Lieto M. Tonelli 《Applied physics. B, Lasers and optics》2002,74(6):607-611
We report the first continuous-wave tunable over ∼280 nm around 2.3 μm room-temperature operation of a chemical vapor transport-grown
and diffusion-doped Cr2+:ZnS laser, pumped by a Co:MgF2 laser at 1.67 μm and generating over 100 mW of output power at 16% slope efficiency. The self-consistent results of the laser
and spectroscopic analysis demonstrate a large potential of this crystal as an active medium for diode-pumped tunable mid-infrared
sources.
Received: 7 January 2002 / Revised: 14 March 2002 / Published online: 2 May 2002 相似文献
7.
《Nuclear Physics B》2002,635(3):435-472
We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p=2,3,5,7 and the other of order pk for k=1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients is either constant or is a hauptmodul for an explicitly found modular fixing group of genus zero. We thus confirm in the cases considered the Generalised Moonshine conjectures for all rational modular functions for the Monster centralisers related to the Baby Monster, Fischer, Harada-Norton and Held sporadic simple groups. We also derive non-trivial constraints on the possible Monster conjugacy classes to which the elements of the orbifolding abelian group may belong. 相似文献
8.
D-branes from matrix factorizations 总被引:1,自引:0,他引:1
B-type D-branes can be obtained from matrix factorizations of the Landau–Ginzburg superpotential. We here review this promising approach to learning about the spacetime superpotential of Calabi–Yau compactifications. We discuss the grading of the D-branes, and present applications in two examples: the two-dimensional torus, and the quintic. To cite this article: K. Hori, J. Walcher, C. R. Physique 5 (2004).
Résumé
Les D-branes de type B peuvent être décrites à partir de factorisations matricielles du super-potentiel de Landau–Ginzburg. On revoit ici cette approche prometteuse pour étudier le super-potentiel en espace-temps de compactifications de Calabi–Yau. On discute la graduation des D-branes, et présente deux exemples : le tore en deux dimensions, ainsi que la quintique. Pour citer cet article : K. Hori, J. Walcher, C. R. Physique 5 (2004). 相似文献9.
We consider both periodic and quasi-periodic solutions for the standard map, and we study the corresponding conjugating functions,
i.e. the functions conjugating the motions to trivial rotations. We compare the invariant curves with rotation numbers ω satisfying
the Bryuno condition and the sequences of periodic orbits with rotation numbers given by their convergents ω
N
= p
N
/q
N
. We prove the following results for N→ ∞: (1) for rotation numbers ω
N
N we study the radius of convergence of the conjugating functions and we find lower bounds on them, which tend to a limit
which is a lower bound on the corresponding quantity for ω; (2) the periodic orbits consist of points which are more and more
close to the invariant curve with rotation number ω; (3) such orbits lie on analytical curves which tend uniformly to the
invariant curve.
Received: 14 December 2001 / Accepted: 16 March 2002?Published online: 2 October 2002 相似文献
10.
E.C. Richard K.K. Kelly R.H. Winkler R. Wilson T.L. Thompson R.J. McLaughlin A.L. Schmeltekopf A.F. Tuck 《Applied physics. B, Lasers and optics》2002,75(2-3):183-194
We describe a near-infrared in situ tunable diode laser spectrometer developed for atmospheric measurements of CH4 in the upper troposphere and lower stratosphere (UT/LS). The instrument is designed to provide fast-response (0.5–1 Hz) measurements
and operate autonomously on the NASA WB-57F high-altitude aircraft. A single-mode InGaAsP distributed feedback laser diode
operating at 1.6537 μm scans continuously over the R(3) rotation–vibration transition in the 2ν3 band. We use a direct absorption technique incorporating a custom-designed long path length (252 m) low-volume (3.6 L) astigmatic
Herriott cell. The present detection sensitivity is 5×1010 molecules cm-3, corresponding to ∼20 ppbv in the UT/LS, with the main limit to instrument precision being background optical interference
fringes. In-flight performance is demonstrated by presentation of recent data.
Received: 25 January 2002 / Revised version: 5 April 2002 / Published online: 21 August 2002
RID="*"
ID="*"Corresponding author. Fax: +1-303/497-5373, E-mail: richard@al.noaa.gov 相似文献
11.
We report on the first layer growth of a Mn6+-doped material. Large-size BaSO4 substrates of 10×6×4 mm3 were grown from a LiCl solvent by the flux method. Flat surfaces of undoped BaSO4 were then achieved by use of liquid-phase epitaxy (LPE) from a CsCl–KCl–NaCl solvent. Finally, BaSO4:Mn6+ layers were grown by LPE with growth velocities of approximately 3 μm h-1, at temperatures of 550–508 °C. Absorption, luminescence, luminescence-excitation and luminescence-decay measurements confirmed
the incorporation of manganese solely in its hexavalent oxidation state. This material possesses potential as a near-infrared
tunable laser with a wavelength range larger than Ti:sapphire.
Received: 7 January 2002 / Revised version: 30 March 2002 / Published online: 8 August 2002 相似文献
12.
We consider the quasi-geostrophic equation with the dissipation term, κ (-Δ)α θ, In the case , Constantin-Cordoba-Wu [6] proved the global existence of strong solution in H
1
and H
2
under the assumption of small L
∞
-norm of initial data. In this paper, we prove the global existence in the scale invariant Besov space, B
2−2α
2,1
, for initial data small in the B
2−2α
2,1
norm. We also prove a global stability result in B
1
2,1
.
Received: 24 April 2002 / Accepted: 29 July 2002 Published online: 10 December 2002
Communicated by P. Constantin 相似文献
13.
We introduce a quantum Minkowski space-time based on the quantum group SU(2)
q
extended by a degree operator and formulate a quantum version of the anti-self-dual Yang-Mills equation. We construct solutions
of the quantum equations using the classical ADHM linear data, and conjecture that, up to gauge transformations, our construction yields all the solutions. We also find
a deformation of Penrose's twistor diagram, giving a correspondence between the quantum Minkowski space-time and the classical
projective space ℙ3.
Received: 10 May 2002 / Accepted: 10 January 2003
Published online: 5 May 2003
Communicated by L. Takhtajan 相似文献
14.
S.L. Woronowicz proved in 1991 that quantum SU(1,1) does not exist as a locally compact quantum group. Results by L.I. Korogodsky
in 1994 and more recently by Woronowicz gave strong indications that the normalizer of SU(1,1) in SL(2,ℂ) is a much better quantization candidate than SU(1,1) itself. In this paper we show that this is indeed the case by constructing , a new example of a unimodular locally compact quantum group (depending on a parameter 0<q<1) that is a deformation of . After defining the underlying von Neumann algebra of we use a certain class of q-hypergeometric functions and their orthogonality relations to construct the comultiplication. The coassociativity of this
comultiplication is the hardest result to establish. We define the Haar weight and obtain simple formulas for the antipode
and its polar decomposition. As a final result we produce the underlying C
*
-algebra of . The proofs of all these results depend on various properties of q-hypergeometric 1ϕ1 functions.
Received: 28 June 2001 / Accepted: 25 July 2002 Published online: 10 December 2002
RID="*"
ID="*" Post-doctoral researcher of the Fund for Scientific Research – Flanders (Belgium) (F.W.O.)
Communicated by L. Takhtajan 相似文献
15.
Results are given for thermal tuning and modulation of a 1556-nm distributed feedback fibre laser by resistive heating of
a thin silver film chemically deposited on the fibre. Without reaching the limits of performance, linear tuning is demonstrated
at a rate of 1.72 pm/mW up to about 200 pm, and a peak-to-peak modulation of 100 MHz up to modulation frequencies of 60 Hz.
The heat flow is analyzed, and the coated fibre is characterized in terms of the static and dynamic wavelength response to
the applied electric power. The performance of the scheme is tested by recording part of the ν1+ν3 combination band spectrum of 13C2H2 with thermal modulation and scanning of the fibre laser.
Received: 12 March 2002 / Revised version: 24 June 2002 / Published online: 25 September 2002
RID="*"
ID="*"Corresponding author. Fax: +45/4593-1137, E-mail: sus@dfm.dtu.dk 相似文献
16.
We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions,
and show that in the quantum theory a remnant survives of the bulk quantized affine algebra symmetry generated by non-local
charges. The paper also develops a general framework for obtaining solutions of the reflection equation by solving an intertwining
property for representations of certain coideal subalgebras of U
q
(ĝ).
Received: 10 December 2001 / Accepted: 7 October 2002 Published online: 19 December 2002 相似文献
17.
Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose 𝔸
h
(M) is a 𝕌
h
(g)-equivariant quantization of the function algebra 𝔸(M) on M. We develop a method of building 𝕌
h
(g)-equivariant quantization on G-orbits in M as quotients of 𝔸
h
(M). We are concerned with those quantizations that may be simultaneously represented as subalgebras in 𝕌*
h
(g) and quotients of 𝔸
h
(M). It turns out that they are in one-to-one correspondence with characters of the algebra 𝔸
h
(M). We specialize our approach to the situation g=gl(n,ℂ), M=End(ℂ
n
), and 𝔸
h
(M) the so-called reflection equation algebra associated with the representation of 𝕌
h
(g) on ℂ
n
. For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and
bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the 𝕌(g)-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits.
Received: 28 April 2002 / Accepted: 3 October 2002 Published online: 24 January 2003
RID="*"
ID="*" This research is partially supported by the Israel Academy of Sciences grant no. 8007/99-01.
Communicated by L. Takhtajan 相似文献
18.
Remco van der Hofstad Frank den Hollander Gordon Slade 《Communications in Mathematical Physics》2002,231(3):435-461
We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ
d
× ℤ+, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ
n
(E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n) ℤ
d
× ℤ+, summing this probability over x ℤ
d
, and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation
to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n
−1, we prove existence of a limiting measure ℚ∞, with ℚ∞ = ℙ∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension
of the cluster of the origin, under ℙ∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented
percolation to super-Brownian motion, for d+1 > 4+1.
Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002
RID="*"
ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513,
5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl 相似文献
19.
20.
Z.J. Li H.J. Li X.L. Chen A.L. Meng K.Z. Li Y.P. Xu L. Dai 《Applied Physics A: Materials Science & Processing》2003,76(4):637-640
Large quantities of high-purity crystalline β-SiC nanowires have been synthesized at relatively low temperature via a new
simple method, the chemical-vapor-reaction approach, in a home-made graphite reaction cell. A mixture of milled Si and SiC
powders and C3H6 were employed as the starting materials. The results show that the nanowires with diameters of about 10–35 nm are single
crystalline β-SiCwithout any wrapping of amorphous material, and the nanowire axes lie along the 〈111〉 direction. Some unique
properties are found in the Raman scattering from the β-SiC nanowires, which are different from previous observations of β-SiC
materials. A possible growth mechanism for the β-SiC nanowires is proposed.
Received: 27 August 2002 / Accepted: 28 August 2002 / Published online: 4 December 2002
RID="*"
ID="*"Corresponding author. Fax: +86-29/8491-000, E-mail: zjli-sohu@sohu.com 相似文献