Related papers: Character sheaves for classical graded Lie algebra…
In this paper we introduce a new ingredient, invariant systems of differential equations, to our study of character sheaves on graded Lie algebras. The character sheaves we construct in this paper, together with the ones constructed in…
We show in this paper that in the context of graded Lie algebras, all cuspidal character sheaves arise from a nearby-cycle construction followed by a Fourier--Sato transform in a very specific manner. Combined with results of the last two…
In this paper we give a complete classification of cyclically graded semisimple Lie algebras that afford cuspidal character sheaves and determine the support of the cuspidal character sheaves. This constitutes a major step towards the…
In this paper we construct full support character sheaves for stably graded Lie algebras. Conjecturally these are precisely the cuspidal character sheaves. Irreducible representations of Hecke algebras associated to complex reflection…
We determine cuspidal character sheaves explicitly for all (GIT) stably graded exceptional Lie algebras.
We describe the isomorphism classes of infinite-dimensional graded Lie algebras of maximal class, generated by elements of weight one, over fields of odd characteristic.
We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…
For sufficiently high dimensions, the naturally graded nonsplit nilpotent Lie algebras with linear characteristic sequence are classified.
We describe the isomorphism classes of certain infinite-dimensional graded Lie algebras of maximal class, generated by an element of weight one and an element of weight two, over fields of odd characteristic.
We give an explicit description of character sheaves for the symmetric pairs associated to inner involutions of the special linear groups. We make use of the general strategy given in [VX1] and central character consideration. We also…
This paper is an introduction, in a simplified setting, to Lusztig's theory of character sheaves. It develops a notion of character sheaves on reductive Lie algebras which is more general then such notion of Lusztig, and closer to Lusztig's…
We classify, up to isomorphism, the group gradings on the non-exceptional classical simple Lie superalgebras, except for type A(1,1), over an algebraically closed field of characteristic zero. To this end, we study graded-simple and…
We investigate the graded Lie algebras of Cartan type $W$, $S$ and $H$ in characteristic 2 and determine their simple constituents and some exceptional isomorphisms between them. We also consider the graded Lie algebras of Cartan type $K$…
In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…
We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.
We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are…
Characteristic Lie algebras of semi-discrete chains are studied. The attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.
Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold…
In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Virasoro algebras. In particular,the derivation algebras, the automorphism groups and the second cohomology groups of these…
We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical…