共查询到20条相似文献,搜索用时 15 毫秒
1.
Minxian Zhu 《Advances in Mathematics》2008,219(5):1513-1547
Let G be a simply-connected complex Lie group with simple Lie algebra g and let be its affine Lie algebra. We use intertwining operators and Knizhnik-Zamolodchikov equations to construct a family of N-graded vertex operator algebras (VOAs) associated to g. These vertex operator algebras contain the algebra of regular functions on G as the conformal weight 0 subspaces and are -modules of dual levels in the sense that , where h∨ is the dual Coxeter number of g. This family of VOAs was previously studied by Arkhipov-Gaitsgory and Gorbounov-Malikov-Schechtman from different points of view. We show that when k is irrational, the vertex envelope of the vertex algebroid associated to G and the level k is isomorphic to the vertex operator algebra we constructed above. The case of rational levels is also discussed. 相似文献
2.
Xu Xiang 《数学学报(英文版)》1997,13(2):161-168
In this paper we study the pointed representations of the Virasoro algebra. We show that unitary irreducible pointed representations
of the Virasoro algebra are Harish-Chandra representations, thus they either are of highest or lowest weights or have all
weight spaces of dimension 1. Further, we prove that unitary irreducible weight representations of Virasoro superalgebras
are either of highest weights or of lowest weights, hence they are also Harish-Chandra representations.
This work was supported by CNSF 相似文献
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I. V. Mikityuk 《Ukrainian Mathematical Journal》1990,42(4):472-477
We investigate Verma modules V over the generalized Virasoro current algebrag, which is the semidirect sum of the Virasoro algebra and the central extension of a commutative algebra. It is shown that an arbitrary unitary representation with highest weight of algebrag is isomorphic to the tensor product of a unitary Fock representation ofg (or of a one-dimensional representation ofg) and a unitary representation with highest weight of the Virasoro algebra (considered as a representation of algebrag). This result is used to obtain formulas for the determinants of the matrices defining the Shapovalov form on Verma module V.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 532–538, April, 1990. 相似文献
5.
Igor B. Frenkel 《Advances in Mathematics》2006,206(1):57-111
We find a counterpart of the classical fact that the regular representation R(G) of a simple complex group G is spanned by the matrix elements of all irreducible representations of G. Namely, the algebra of functions on the big cell G0⊂G of the Bruhat decomposition is spanned by matrix elements of big projective modules from the category O of representations of the Lie algebra g of G, and has the structure of a g⊕g-module.The standard regular representation of the affine group has two commuting actions of the Lie algebra with total central charge 0, and carries the structure of a conformal field theory. The modified versions and , originating from the loop version of the Bruhat decomposition, have two commuting -actions with central charges shifted by the dual Coxeter number, and acquire vertex operator algebra structures derived from their Fock space realizations, given explicitly for the case G=SL(2,C).The quantum Drinfeld-Sokolov reduction transforms the representations of the affine Lie algebras into their W-algebra counterparts, and can be used to produce analogues of the modified regular representations. When g=sl(2,C) the corresponding W-algebra is the Virasoro algebra. We describe the Virasoro analogues of the modified regular representations, which are vertex operator algebras with the total central charge equal to 26.The special values of the total central charges in the affine and Virasoro cases lead to the non-trivial semi-infinite cohomology with coefficients in the modified regular representations. The inherited vertex algebra structure on this cohomology degenerates into a supercommutative associative superalgebra. We describe these superalgebras in the case when the central charge is generic, and identify the 0th cohomology with the Grothendieck ring of finite-dimensional G-modules. We conjecture that for the integral values of the central charge the 0th semi-infinite cohomology coincides with the Verlinde algebra and its counterpart associated with the big projective modules. 相似文献
6.
We announce the construction of an explicit basis for all integrable highest weight modules over the Lie algebra A
1
(1). The construction uses representations of vertex operator algebras and leads to combinatorial identities of Rogers-Ramanujan-type. 相似文献
7.
B. L. Feigin 《Functional Analysis and Its Applications》2011,45(4):297-304
We construct a resolution that permits computing the t-character of representations of the Virasoro algebra from the (2, 2p + 1)-models, i.e., the characters of the associated graded spaces with respect to the Poincaré-Birkhoff-Witt filtration. 相似文献
8.
Weiqiang Wang 《中国科学 数学(英文版)》2018,(2)
We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine sl_2 and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset construction for affine sl_2 is valid. 相似文献
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V. Yu. Ovsienko 《Functional Analysis and Its Applications》1990,24(4):306-314
CNRS, Centre de Physique Théorique, Luminy, Marseille, France. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 24, No. 4, pp. 54–62, October–December, 1990. 相似文献
11.
A. U. Klimyk 《Mathematical Notes》1970,8(6):868-871
A formula is derived for the decomposition of the highest-weight representation of a semisimple Lie algebra into irreducible representations of its regular subalgebra. In particular the case of finite-dimensional representations is investigated.Translated from Matematicheskie Zametki, Vol. 8, No. 6, pp. 703–710, December, 1970. 相似文献
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Luc Haine Didier Vanderstichelen 《Journal of Computational and Applied Mathematics》2011,236(1):19-27
We consider the 2-dimensional Toda lattice tau functions τn(t,s;η,θ) deforming the probabilities τn(η,θ) that a randomly chosen matrix from the unitary group U(n), for the Haar measure, has no eigenvalues within an arc (η,θ) of the unit circle. We show that these tau functions satisfy a centerless Virasoro algebra of constraints, with a boundary part in the sense of Adler, Shiota and van Moerbeke. As an application, we obtain a new derivation of a differential equation due to Tracy and Widom, satisfied by these probabilities, linking it to the Painlevé VI equation. 相似文献
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苏育才 《中国科学A辑(英文版)》2001,44(8):980-983
It is proved that an indecomposable Harish- Chandra module over the Virasoro algebra must be (i) a uniformly bounded module,
or (ii) a module in Category
, or (iii) a module in Category
, or ( iv) a module which contains the trivial module as one of its composition factors. 相似文献
16.
Gabriele Nebe 《Journal of Number Theory》2009,129(3):588-603
An algebra H(Gm) of double cosets is constructed for every finite Weil representation Gm. For the Clifford-Weil groups Gm=Cm(ρ) associated to some classical Type ρ of selfdual codes over a finite field, this algebra is shown to be commutative. Then the eigenspace decomposition of H(Cm(ρ)) acting on the space of degree N invariants of Cm(ρ) may be obtained from the kernels of powers of the coding theory analogue of the Siegel Φ-operator. 相似文献
17.
M. W. Wong 《Proceedings of the American Mathematical Society》2002,130(10):2911-2919
We prove an boundedness result for localization operators associated to left regular representations of locally compact and Hausdorff groups and give an application to wavelet multipliers.
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E. H. El Kinani 《Advances in Applied Clifford Algebras》2003,13(2):127-131
In this paper we construct the quantum Virasoro algebra
generators in terms of operators of the generalized Clifford algebras Cnk. Precisely, we show that
can be embedded into generalized Clifford algebras.
Junior Associate at The Abdus Salam ICTP, Trieste, Italy. 相似文献