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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
JOSEPH IDEALS AND LISSE MINIMAL $W$ -ALGEBRAS
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
CHIRAL ALGEBRAS OF CLASS S AND MOORE-TACHIKAWA SYMPLECTIC 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
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