We prove the existence of a homomorphism vertex algebras, from vacuum Verma module over loop algebra an untwisted affine algebra, whose construction is analogous to that Feigin-Frenkel at critical level algebra.

We construct a generator system of the annihilator of the generalized Verma module of gl(n,C) induced from any character of any parabolic subalgebra as an analogue of minors and elementary divisors. The generator system has a quantization parameter ε and it generates the defining ideal of the conjugacy class of square matrices at the classical limit ε = 0.

In this article we prove that for a basic classical Lie superalgebra the annihilator of a strongly typical Verma module is a centrally generated ideal. For a basic classical Lie superalgebra of type I we prove that the localization of the enveloping algebra by a certain central element is free over its centre.

We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series of simple Lie groups and some exceptional finite simple groups including the Monster and Baby Monster.

We construct a family of exact functors from the BGG category O of representations of the Lie algebra sln(C) to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra Hl of GLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simple Hl-module can be thus obtained.

In this paper complexes of generalized Verma modules over the infinitedimensional exceptional Lie superalgebras E(3, 8) and E(5, 10) are constructed and studied. 0. Introduction. In our papers [KR1]–[KR3] we constructed all degenerate irreducible modules over the exceptional Lie superalgebra E(3, 6). In the present paper we apply the same method to the exceptional Lie superalgebras E(3, 8) and ...

We prove that the following two categories of sl(n,C)-modules are equivalent: 1) the category of modules with integral support filtered by submodules of Verma modules and complete with respect to Enright’s completion functor; 2) the category of all subquotients of modules F ⊗ M , where F is a finite-dimensional module and M is a fixed simple generic Gelfand-Zetlin module with integral central c...

We construct the action of the quantum group Uv(sln) by the natural correspondences in the equivariant localized K-theory of the Laumon based Quasiflags’ moduli spaces. The resulting module is the universal Verma module. We construct geometrically the Shapovalov scalar product and the Whittaker vectors. It follows that a certain generating function of the characters of the global sections of th...

We show that the Jantzen filtration of a Verma module (possibly singular) coincides with its radical filtration. It implies Conjecture on modules holds for all infinitesimal characters, while regular case was settled by Beilinson and Bernstein geometric methods reproved Williamson an algebraic approach.