共查询到20条相似文献,搜索用时 31 毫秒
1.
Quantum Conjugacy Classes of Simple Matrix Groups 总被引:1,自引:0,他引:1
A. Mudrov 《Communications in Mathematical Physics》2007,272(3):635-660
Let G be a simple complex classical group and its Lie algebra. Let be the Drinfeld-Jimbo quantization of the universal enveloping algebra . We construct an explicit -equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers.
Dedicated to the memory of Joseph Donin
This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany,
the Excellency Center “Group Theoretic Methods in the study of Algebraic Varieties” of the Israel Science foundation, by the
EPSRC grant C511166, and by the RFBR grant no. 06-01-00451. 相似文献
2.
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
3.
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
4.
We introduce a newfamily of C
2-cofinite N = 1 vertex operator superalgebras , m ≥ 1, which are natural super analogs of the triplet vertex algebra family , p ≥ 2, important in logarithmic conformal field theory. We classify irreducible -modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible characters. Finally, we contemplate possible connections between the category of -modules and the category of modules for the quantum group , , by focusing primarily on properties of characters and the Zhu’s algebra . This paper is a continuation of our paper Adv. Math. 217, no.6, 2664–2699 (2008).
The second author was partially supported by NSF grant DMS-0802962. 相似文献
5.
We use the technique of Harish-Chandra bimodules to prove that regular strongly typical blocks of the category for the queer Lie superalgebra are equivalent to the corresponding blocks of the category for the Lie algebra . 相似文献
6.
7.
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
8.
Svea Beiser Hartmann Römer Stefan Waldmann 《Communications in Mathematical Physics》2007,272(1):25-52
We construct a Fréchet space as a subspace of where the Wick star product converges and is continuous. The resulting Fréchet algebra
ħ
is studied in detail including a *-representation of
ħ
in the Bargmann-Fock space and a discussion of star exponentials and coherent states. 相似文献
9.
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
10.
A Negative Mass Theorem for the 2-Torus 总被引:1,自引:1,他引:0
K. Okikiolu 《Communications in Mathematical Physics》2008,284(3):775-802
Let M be a closed surface. For a metric g on M, denote the area element by dA and the Laplace-Beltrami operator by Δ = Δ
g
. We define the Robin mass m(p) at the point to be the value of the Green function G(p, q) at q = p after the logarithmic singularity has been subtracted off, and we define trace . This regularized trace can also be obtained by regularization of the spectral zeta function and is hence a spectral invariant
which heuristically measures the total wavelength of the surface.We define the Δ-mass of (M, g) to equal , where is the Laplacian on the round sphere of area A. This scale invariant quantity is a non-trivial analog for closed surfaces of the ADM mass for higher dimensional asymptotically
flat manifolds.In this paper we show that in each conformal class for the 2-torus, there exists a metric with negative Δ-mass. From this it follows that the minimum of the Δ-mass on is negative and attained by some metric . For this minimizing metric g, one gets a sharp logarithmic Hardy-Littlewood-Sobolev inequality and an Onofri-type inequality.We remark that if the flat
metric in is sufficiently long and thin then the minimizing metric g is non-flat. The proof of our result depends on analyzing the ordinary differential equation which is equivalent to h′′ = 1 − 1/h. The solutions are periodic and we need to establish quite delicate, asymptotically sharp inequalities relating the period
to the maximum value.
The author was supported by the National Science Foundation #DMS-0302647. 相似文献
11.
H. Boos M. Jimbo T. Miwa F. Smirnov Y. Takeyama 《Communications in Mathematical Physics》2007,272(1):263-281
For the critical XXZ model, we consider the space of operators which are products of local operators with a disorder operator. We introduce two anti-commutative families of
operators which act on . These operators are constructed as traces over representations of the q-oscillator algebra, in close analogy with Baxter’s Q-operators. We show that the vacuum expectation values of operators in can be expressed in terms of an exponential of a quadratic form of .
On leave of absence from Skobeltsyn Institute of Nuclear Physics, MSU, 119992, Moscow, Russia
Membre du CNRS 相似文献
12.
Lucy Gow 《Communications in Mathematical Physics》2007,276(3):799-825
We describe a Gauss decomposition for the Yangian of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie
superalgebra Y(A(m − 1, n − 1)) (for m ≠ n) defined and studied in papers by Stukopin, and suggests natural definitions for the Yangians and Y(A(n, n)). We also show that the coefficients of the quantum Berezinian generate the centre of the Yangian . This was conjectured by Nazarov in 1991. 相似文献
13.
Claude Cibils Andrea Solotar Robert Wisbauer 《Communications in Mathematical Physics》2007,272(3):837-849
We consider -complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then
to prove that amplitude cohomology (called generalized cohomology by M. Dubois-Violette) only vanishes on injective functors
providing a well defined functor on the stable category. For left truncated -complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover
amplitude cohomology of positive -complexes is proved to be isomorphic to an Ext functor of an indecomposable -complex inside the abelian functor category. Finally we show that for the monoidal structure of -complexes a Clebsch-Gordan formula holds, in other words the fusion rules for -complexes can be determined.
This work has been supported by the projects PICT 08280 (ANPCyT), UBACYTX169, PIP-CONICET 5099 and the German Academic Exchange
Service (DAAD). The second author is a research member of CONICET (Argentina) and a Regular Associate of ICTP Associate Scheme. 相似文献
14.
S. M. Khoroshkin I. I. Pop M. E. Samsonov A. A. Stolin V. N. Tolstoy 《Communications in Mathematical Physics》2008,282(3):625-662
We study classical twists of Lie bialgebra structures on the polynomial current algebra , where is a simple complex finite-dimensional Lie algebra. We focus on the structures induced by the so-called quasi-trigonometric
solutions of the classical Yang-Baxter equation. It turns out that quasi-trigonometric r-matrices fall into classes labelled by the vertices of the extended Dynkin diagram of . We give the complete classification of quasi-trigonometric r-matrices belonging to multiplicity free simple roots (which have coefficient 1 in the decomposition of the maximal root).
We quantize solutions corresponding to the first root of . 相似文献
15.
We consider a class of singular Riemannian manifolds, the deformed spheres , defined as the classical spheres with a one parameter family g[k] of singular Riemannian structures, that reduces for k = 1 to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian
, we study the associated zeta functions . We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the
ones appearing in . An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and
in particular and . We give explicit formulas for the zeta regularized determinant in the low dimensional cases, N = 2,3, thus generalizing a result of Dowker [25], and we compute the first coefficients in the expansion of these determinants
in powers of the deformation parameter k.
Partially supported by FAPESP: 2005/04363-4 相似文献
16.
Adrian Butscher 《Communications in Mathematical Physics》2007,272(1):1-23
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial
data hypersurface in an asymptotically simple space-time satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The
extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the
second fundamental form and two other tensorial quantities defined on , and are equivalent to the usual constraint equations that satisfies as a space-like hypersurface in a space-time satisfying Einstein’s vacuum equation. This article develops a method
for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat
solution on Euclidean space. This method is fundamentally different from the ‘classical’ method of Lichnerowicz and York that
is used to solve the usual constraint equations. 相似文献
17.
Serban Belinschi Amir Dembo Alice Guionnet 《Communications in Mathematical Physics》2009,289(3):1023-1055
We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N × N symmetric matrix whose (i, j) entry is , where (x
ij
, 1 ≤ i ≤ j < ∞) is an infinite array of i.i.d real variables with common distribution in the domain of attraction of an α-stable law, , and σ is a deterministic function. For random diagonal D
N
independent of and with appropriate rescaling a
N
, we prove that converges in mean towards a limiting probability measure which we characterize. As a special case, we derive and analyze
the almost sure limiting spectral density for empirical covariance matrices with heavy tailed entries.
Supported in part by a Discovery grant from the Natural Sciences and Engineering Research Council of Canada and a University
of Saskatchewan start-up grant.
Research partially supported by NSF grant #DMS-0806211. 相似文献
18.
S. Lievens N. I. Stoilov J. Van der Jeugt 《Communications in Mathematical Physics》2008,281(3):805-826
It is known that the defining relations of the orthosymplectic Lie superalgebra are equivalent to the defining (triple) relations of n pairs of paraboson operators . In particular, with the usual star conditions, this implies that the “parabosons of order p” correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V(p) of . Apart from the simple cases p = 1 or n = 1, these representations had never been constructed due to computational difficulties, despite their importance. In the
present paper we give an explicit and elegant construction of these representations V(p), and we present explicit actions or matrix elements of the generators. The orthogonal basis vectors of V(p) are written in terms of Gelfand-Zetlin patterns, where the subalgebra of plays a crucial role. Our results also lead to character formulas for these infinite-dimensional representations. Furthermore, by considering the branching , we find explicit infinite-dimensional unitary irreducible lowest weight representations of and their characters.
NIS was supported by a project from the Fund for Scientific Research – Flanders (Belgium) and by project P6/02 of the Interuniversity
Attraction Poles Programme (Belgian State – Belgian Science Policy).
An erratum to this article can be found at 相似文献
19.
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
20.
Bloch and Okounkov introduced an n-point correlation function on the infinite wedge space and found an elegant closed formula in terms of theta functions. This
function has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc., and it can also be interpreted
as correlation functions on integrable -modules of level one. Such -correlation functions at higher levels were then calculated by Cheng and Wang.
In this paper, generalizing the type A results, we formulate and determine the n-point correlation functions in the sense of Bloch-Okounkov on integrable modules over classical Lie subalgebras of of type B, C, D at arbitrary levels. As byproducts, we obtain new q-dimension formulas for integrable modules of type B, C, D and some fermionic type q-identities. 相似文献