Related papers: The primitive spectrum of basic classical Lie supe…

With an eye to applications to type A and Schur-Weyl duality, we study Kazhdan-Lusztig bases for a general parabolic Hecke algebra. Parabolic Hecke algebras are idempotent subalgebras of Hecke algebras corresponding to parabolic subgroups,…

Brown and Goodearl stated a conjecture that provides an explicit description of the topology of the spectra of quantum algebras. The conjecture takes on a more explicit form if there exist separating Ore sets for all incident pairs of torus…

In this paper we use the Etingof-Kazhdan quantization of Lie bi-superalgebras to investigate some interesting questions related to Drinfeld-Jimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that…

We define contragredient Lie algebras in symmetric categories, generalizing the construction of Lie algebras of the form $\mathfrak{g}(A)$ for a Cartan matrix $A$ from the category of vector spaces to an arbitrary symmetric tensor category.…

Two decades ago P. Martin and D. Woodcock made a surprising and prophetic link between statistical mechanics and representation theory. They observed that the decomposition numbers of the blob algebra (that appeared in the context of…

Prototypical rational vertex operator algebras are associated to affine Lie algebras at positive integer level k. They correspond physically to the Wess-Zumino-Witten theories, and their representation theory can be captured by quantum…

Let d \subset d' be finite-dimensional Lie algebras, H = U(d), H'=U(d') the corresponding universal enveloping algebras endowed with the cocommutative Hopf algebra structure. We show that if L is a primitive Lie pseudoalgebra over H then…

In the present article we discuss the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra $\mathfrak{g}$. This problem reduces to the classification of all Lie bialgebra structures on…

We show that, for many Lie superalgebras admitting a compatible $\mathbb{Z}$-grading, Kac induction functor gives rise to a bijection between simple supermodules over a Lie superalgebra and simple supermodules over the even part of this Lie…

Using the results of J. Arthur on the representation theory of classical groups with additional work by Colette Moeglin and its relation with representations of affine Hecke algebras established by the author, we show that the category of…

Fix an integral semisimple element $\lambda$ in the Lie algebra $\mathfrak{g}$ of a complex reductive algebraic group $G$. Let $L$ denote the centralizer of $\lambda$ in $G$ and let $\mathfrak{g}(-1)$ denote the $-1$ eigenspace of…

We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all…

We introduce the notion of minimal reduction type of an affine Springer fiber, and use it to define a map from the set of conjugacy classes in the Weyl group to the set of nilpotent orbits. We show that this map is the same as the one…

For an Artinian $(n-1)$-Auslander algebra $\Lambda$ with global dimension $n(\geq 2)$, we show that if $\Lambda$ admits a trivial maximal $(n-1)$-orthogonal subcategory of $\mod\Lambda$, then $\Lambda$ is a Nakayama algebra and the…

Let $\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent orbit $\cal O$ in $\FRAK{g}_0$ we associate a Clifford algebra over the field of rational functions on $\cal O$. We find the rank, $k(\cal O)$ of the bilinear form…

The center of a semisimple Lie algebra can be described as the algebra of W-invariant functions on the dual of the Cartan subalgebra. The centers of many Lie superalgebras have a similar description, but the defining equivalence relation on…

The prime spectra of two families of algebras, $S^w$ and $\check{S}^w$, $w\in W,$ indexed by the Weyl group $W$ of a semisimple finitely dimensional are studied. The algebras $S^w$ have been introduced by A.~Joseph; they are $q$-analogues…

For a semisimple Lie algebra defined over a discrete valuation ring with field of fractions $K$, we prove that any primitive ideal with rational central character in the affinoid enveloping algebra, $\widehat{U(\mathfrak{g})_{K}},$ is the…

This paper consists of three parts: (I) To develop general theory of a (large) class of central simple finite dimensional algebras and answering some natural questions about them (that in general situation it is not even clear how to…

We classify simple linearly compact n-Lie superalgebras with n>2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive Z-graded Lie superalgebras…