Representation Theory of W-algebras
نویسنده
چکیده
We study the representation theory of the W-algebra Wk(ḡ) associated with a simple Lie algebra ḡ at level k. We show that the “−” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any level k ∈ C. Moreover, we show that the character of each irreducible highest weight representation of Wk(ḡ) is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra of ḡ. As a consequence we complete (for “−” reduction) the proof of the conjecture of E. Frenkel, V. Kac and M. Wakimoto on the existence and the construction of the modular invariant representations of W-algebras. This article is the detailed version of [2] with extended results.
منابع مشابه
ON THE USE OF KULSHAMMER TYPE INVARIANTS IN REPRESENTATION THEORY
Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...
متن کاملHopf Algebras, Symmetric Functions and Representations
1.1. Motivation. Much of representation theory can be unified by considering the representation theory of associative algebras. Specifically, the representation theory of Lie algebras may be studied via the representations of universal enveloping algebras; the representation theory of finite groups studied via the representation theory of the group algebra; the representation theory of quivers ...
متن کاملTHE DUALITY OF THE L?-REPRESENTATION ALGEBRA ?(S ) OF A FOUNDATION SEMIGROUP S AND FUNCTION ALGEBRAS
In the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(S) is the dual of a function algebra.
متن کاملRepresentation Theory of Symmetric Groups and Related Hecke Algebras
We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via categorification. We present results on branching rules and crystal graphs, decomposition numbers and canonical bases, graded representation theory, connections with cyclotomic and affine Hecke alge...
متن کاملWeighted Convolution Measure Algebras Characterized by Convolution Algebras
The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.
متن کاملEndomorphismalgebras and Representation Theory
Endomorphism algebras gure prominently in group representation theory. F or example, if G is a nite group of Lie type, the representation theory of the endomorphism algebra End G Cj G B |sometimes known as the Hecke algebra over C of G|plays a central role in unraveling the complex unipotent c haracters on G 22, 77. Another example arises in the modular representation theory of the nite general...
متن کامل