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Duality between sln(C) and the Degenerate Affine Hecke Algebra
Abstract We construct a family of exact functors from the Bernstein–Gelfand–Gelfand category O of s l n-modules to the category of finite-dimensional representations of the degenerate affine Hecke
Rationality of W-algebras: principal nilpotent cases
We prove the rationality of all the minimal series principal W -algebras discovered by Frenkel, Kac and Wakimoto, thereby giving a new family of rational and C2-conite vertex operator algebras. A key
Rationality of Bershadsky-Polyakov Vertex Algebras
We prove the conjecture of Kac-Wakimoto on the rationality of exceptional W-algebras for the first non-trivial series, namely, for the Bershadsky-Polyakov vertex algebras $${W_3^{(2)}}$$W3(2) at
Associated Varieties of Modules Over Kac–Moody Algebras and C2-Cofiniteness of W-Algebras
First, we establish the relation between the associated varieties of modules over Kac-Moody algebras \hat{g} and those over affine W-algebras. Second, we prove the Feigin-Frenkel conjecture on the
Representation theory of $\mathcal{W}$-algebras
We study the representation theory of the $\mathcal{W}$-algebra $\mathcal{W}_k(\bar{\mathfrak{g}})$ associated with a simple Lie algebra $\bar{\mathfrak{g}}$ at level k. We show that the “-”
Representation Theory of W-Algebras
This paper is the detailed version of math.QA/0403477 (T. Arakawa, Quantized Reductions and Irreducible Representations of W-Algebras) with extended results; We study the representation theory of
We consider a lifting of Joseph ideals for the minimal nilpotent orbit closure to the setting of affine Kac–Moody algebras and find new examples of affine vertex algebras whose associated varieties
We give a functorial construction of the genus zero chiral algebras of class S, that is, the vertex algebras corresponding to the theory of class S associated with genus zero punctured Riemann
Introduction to W-Algebras and Their Representation Theory
These are lecture notes from author’s mini-course on W-algebras during Session 1: “Vertex algebras, W-algebras, and application” of INdAM Intensive research period “Perspectives in Lie Theory”, at
Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture
We study the representation theory of the superconformal algebra $W_k(g,f_{\theta})$ associated with a minimal gradation of $g$. Here, $g$ is a simple finite-dimensional Lie superalgebra with a