共查询到20条相似文献,搜索用时 15 毫秒
1.
Dražen Adamović 《Communications in Mathematical Physics》2007,270(1):141-161
We introduce the infinite-dimensional Lie superalgebra and construct a family of mappings from a certain category of –modules to the category of –modules at the critical level. Using this approach, we prove the irreducibility of a large family of –modules at the critical level parameterized by . As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give natural realizations
of irreducible quotients of relaxed Verma modules and calculate characters of these representations.
Partially supported by the MZOS grant 0037125 of the Republic of Croatia 相似文献
2.
We construct a continuous transition density of the semigroup generated by for and b in the Kato class on . For small time the transition density is comparable with that of the fractional Laplacian.
Partially supported by KBN and MEN. 相似文献
3.
Markus Heydenreich Remco van der Hofstad 《Communications in Mathematical Physics》2007,270(2):335-358
We investigate the scaling of the largest critical percolation cluster on a large d-dimensional torus, for nearest-neighbor percolation in sufficiently high dimensions, or when d > 6 for sufficiently spread-out percolation. We use a relatively simple coupling argument to show that this largest critical
cluster is, with high probability, bounded above by a large constant times V
2/3 and below by a small constant times , where V is the volume of the torus. We also give a simple criterion in terms of the subcritical percolation two-point function on
under which the lower bound can be improved to small constant times , i.e. we prove random graph asymptotics for the largest critical cluster on the high-dimensional torus. This establishes a conjecture by [1], apart from logarithmic
corrections. We discuss implications of these results on the dependence on boundary conditions for high-dimensional percolation.
Our method is crucially based on the results in [11, 12], where the scaling was proved subject to the assumption that a suitably defined critical window contains the percolation threshold on . We also strongly rely on mean-field results for percolation on proved in [17–20]. 相似文献
4.
We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra
form which we can then ‘quantise’ by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor
space , compactified Minkowski space and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local
form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the
formulation in terms of projective varieties. We outline how the Penrose-Ward transform then quantises. As an example, we
show that the pull-back of the tautological bundle on pulls back to the basic instanton on and that this observation quantises to obtain the Connes-Landi instanton on θ-deformed S
4 as the pull-back of the tautological bundle on our θ-deformed . We likewise quantise the fibration and use it to construct the bundle on θ-deformed that maps over under the transform to the θ-deformed instanton.
The work was mainly completed while S.M. was visiting July-December 2006 at the Isaac Newton Institute, Cambridge, which both
authors thank for support. 相似文献
5.
Indranil Biswas Tomás L. Gómez Norbert Hoffmann Marina Logares 《Communications in Mathematical Physics》2009,290(1):357-369
Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let denote the corresponding Deligne–Hitchin moduli space. We prove that the complex analytic space determines (up to an isomorphism) the unordered pair , where is the Riemann surface defined by the opposite almost complex structure on X. 相似文献
6.
In this paper we introduce Baxter integral -operators for finite-dimensional Lie algebras and . Whittaker functions corresponding to these algebras are eigenfunctions of the -operators with the eigenvalues expressed in terms of Gamma-functions. The appearance of the Gamma-functions is one of the
manifestations of an interesting connection between Mellin-Barnes and Givental integral representations of Whittaker functions,
which are in a sense dual to each other. We define a dual Baxter operator and derive a family of mixed Mellin-Barnes-Givental
integral representations. Givental and Mellin-Barnes integral representations are used to provide a short proof of the Friedberg-Bump
and Bump conjectures for G = GL(ℓ + 1) proved earlier by Stade. We also identify eigenvalues of the Baxter -operator acting on Whittaker functions with local Archimedean L-factors. The Baxter -operator introduced in this paper is then described as a particular realization of the explicitly defined universal Baxter
operator in the spherical Hecke algebra , K being a maximal compact subgroup of G. Finally we stress an analogy between -operators and certain elements of the non-Archimedean Hecke algebra . 相似文献
7.
We define the twisted loop Lie algebra of a finite dimensional Lie algebra
as the Fréchet space of all twisted periodic smooth mappings from
to
. Here the Lie algebra operation is continuous. We call such Lie algebras Fréchet Lie algebras. We introduce the notion of an integrable
-gradation of a Fréchet Lie algebra, and find all inequivalent integrable
-gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.On leave of absence from the Institute for Nuclear Research of the Russian Academy of Sciences, 117312 Moscow, Russia. 相似文献
8.
We exhibit a finitely generated group whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping
class group associated to a surface of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus g with n boundary components, for any g ≥ 0 and n > 0. We construct a representation of into the restricted symplectic group of the real Hilbert space generated by the homology classes of non-separating circles on , which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first
universal Chern class in is the pull-back of the Pressley-Segal class on the restricted linear group via the inclusion .
L. F. was partially supported by the ANR Repsurf:ANR-06-BLAN-0311. 相似文献
9.
Liang Kong 《Communications in Mathematical Physics》2008,283(1):25-92
Let V be a vertex operator algebra satisfying certain reductivity and finiteness conditions such that , the category of V-modules, is a modular tensor category. We study open-closed field algebras over V equipped with nondegenerate invariant bilinear forms for both open and closed sectors. We show that they give algebras over
a certain -extension of the so-called Swiss-cheese partial dioperad, and we can obtain Ishibashi states easily in such algebras. The
Cardy condition can be formulated as an additional condition on such open-closed field algebras in terms of the action of
the modular transformation on the space of intertwining operators of V. We then derive a graphical representation of S in the modular tensor category . This result enables us to give a categorical formulation of the Cardy condition and the modular invariance condition for
1-point correlation functions on the torus. Then we incorporate these two conditions and the axioms of the open-closed field
algebra over V equipped with nondegenerate invariant bilinear forms into a tensor-categorical notion called the Cardy -algebra. In the end, we give a categorical construction of the Cardy -algebra in the Cardy case. 相似文献
10.
Consider in the operator family . P
0 is the quantum harmonic oscillator with diophantine frequency vector ω, F
0 a bounded pseudodifferential operator with symbol decreasing to zero at infinity in phase space, and . Then there exist independent of and an open set such that if and , the quantum normal form near P
0 converges uniformly with respect to . This yields an exact quantization formula for the eigenvalues, and for the classical Cherry theorem on convergence of Birkhoff’s normal form for complex frequencies is recovered.
Partially supported by PAPIIT-UNAM IN106106-2. 相似文献
11.
For convex co-compact hyperbolic quotients , we analyze the long-time asymptotic of the solution of the wave equation u(t) with smooth compactly supported initial data f = (f
0, f
1). We show that, if the Hausdorff dimension δ of the limit set is less than n/2, then where and . We explain, in terms of conformal theory of the conformal infinity of X, the special cases , where the leading asymptotic term vanishes. In a second part, we show for all the existence of an infinite number of resonances (and thus zeros of Selberg zeta function) in the strip . As a byproduct we obtain a lower bound on the remainder R(t) for generic initial data f. 相似文献
12.
An Algebra of Deformation Quantization for Star-Exponentials on Complex Symplectic Manifolds 总被引:1,自引:0,他引:1
The cotangent bundle T
*
X to a complex manifold X is classically endowed with the sheaf of k-algebras of deformation quantization, where k := is a subfield of . Here, we construct a new sheaf of k-algebras which contains as a subalgebra and an extra central parameter t. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If P is any section of order zero of , we show that is well defined in . 相似文献
13.
We study a large class of Poisson manifolds, derived from Manin triples, for which we construct explicit partitions into regular
Poisson submanifolds by intersecting certain group orbits. Examples include all varieties of Lagrangian subalgebras of reductive quadratic Lie algebras with Poisson structures defined by Lagrangian splittings of . In the special case of , where is a complex semi-simple Lie algebra, we explicitly compute the ranks of the Poisson structures on defined by arbitrary Lagrangian splittings of . Such Lagrangian splittings have been classified by P. Delorme, and they contain the Belavin–Drinfeld splittings as special
cases. 相似文献
14.
Fuminori Nakata 《Communications in Mathematical Physics》2009,289(2):663-699
We construct infinitely many Einstein-Weyl structures on of signature (− + +) which is sufficiently close to the model case of constant curvature, and on which the space-like geodesics
are all closed. Such a structure is obtained as a parameter space of a family of holomorphic disks which is associated to
a small perturbation of the diagonal of . The geometry of constructed Einstein-Weyl spaces is well understood from the configuration of holomorphic disks. We also
review Einstein-Weyl structures and their properties in the former half of this article.
This work is partially supported by Grant-in-Aid for Scientific Research of the Japan Society for the Promotion of Science. 相似文献
15.
In this paper we investigate the dynamics of relativistic (in particular, closed) strings moving in the Minkowski space
. We first derive a system with n nonlinear wave equations of Born-Infeld type which governs the motion of the string. This system can also be used to describe the extremal surfaces in
. We then show that this system enjoys some interesting geometric properties. Based on this, we give a sufficient and necessary condition for the global existence of extremal surfaces without space-like point in
with given initial data. This result corresponds to the global propagation of nonlinear waves for the system describing the motion of the string in
. We also present an explicit exact representation of the general solution for such a system. Moreover, a great deal of numerical analyses are investigated, and the numerical results show that, in phase space, various topological singularities develop in finite time in the motion of the string. Finally, some important discussions related to the theory of extremal surfaces of mixed type in
are given. 相似文献
16.
17.
Clifford H. Taubes 《Communications in Mathematical Physics》2006,267(1):25-64
I describe a functional integral for maps from
to a Lie group or its quotient which has a simple renormalization that leads to a quantum field theory for maps from
into the Lie group or its quotient whose Hamiltonian is the time translation generator for a unitary action of the n+1 dimensional Poincaré group on the quantum Hilbert space. I also explain how the renormalization provides a functional integral for maps from a Riemann surface to a compact Lie group or its quotient that exhibits many conformal field theoretic properties.Support in part by a grant from the National Science Foundation 相似文献
18.
Jonathan Weitsman 《Communications in Mathematical Physics》2008,277(1):101-125
We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures
are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum
field theory. We give three concrete examples of our construction. The first example is a family of measures on a space of functions on the two-torus, parametrized by a polynomial P (the Wess-Zumino-Landau-Ginzburg model). The second is a family of measures on a space of maps from to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family of measures on the product of a space of connections on the trivial principal bundle with structure group G on a three-dimensional manifold M with a space of -valued three-forms on M.
We show that these measures are positive, and that the measures are Borel probability measures. As an application we show that formulas arising from expectations in the measures reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar
computation for the measures , where M is a homology three-sphere, will yield the Casson invariant of M.
Dedicated to the memory of Raoul Bott
Supported in part by NSF grant DMS 04/05670. 相似文献
19.
Hyun Jae Yoo 《Journal of statistical physics》2007,126(2):325-354
Given a positive definite, bounded linear operator A on the Hilbert space
0≔l
2(E), we consider a reproducing kernel Hilbert space
+ with a reproducing kernel A(x,y). Here E is any countable set and A(x,y), x,y∊ E, is the representation of A w.r.t. the usual basis of
0. Imposing further conditions on the operator A, we also consider another reproducing kernel Hilbert space
− with a kernel function B(x,y), which is the representation of the inverse of A in a sense, so that
−⊃
0⊃
+ becomes a rigged Hilbert space. We investigate the ratios of determinants of some partial matrices of A and B. We also get a variational principle on the limit ratios of these values. We apply this relation to show the Gibbsianness
of the determinantal point process (or fermion point process) defined by the operator A(I+A)−1 on the set E.
2000 Mathematics Subject Classification: Primary: 46E22 Secondary: 60K35 相似文献
20.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献