Representation Theory of W-Algebras

2005/06/03 by Tomoyuki Arakawa, Arakawa, Tomoyuki · 4 citations
Mathematics · #17B68 #81R10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0506056

openalex publication_date 2005/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 the W-algebra W_k(g) associated with a simple Lie algebra g (and its principle nilpotent element) 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. Moreover, we show that the character of each irreducible highest weight representation of W_k(g) is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra of g.

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• Characters and fusion rules of boundary W-algebras
• A tensor category construction of the W_p,q triplet vertex operator algebra and applications
• Inverse Hamiltonian reduction for affine W-algebras in type A
• The affine Brylinski filtration and \mathscrW-algebras

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