Vertex operators and the class algebras of symmetric groups

2001/02/06 by A. Lascoux, Alain Lascoux, Lascoux, A. +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Holomorphic and Operator Theory #math.CO

paper · pdf · doi:10.48550/arxiv.math/0102041

23 pages, LaTex. Minor typos corrected

openalex publication_date 2001/02/06 · arxiv created 2001/06/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit a vertex operator which implements multiplication by power-sums of Jucys-Murphy elements in the centers of the group algebras of all symmetric groups simultaneously. The coefficients of this operator generate a representation of \cal W_1+∞, to which operators multiplying by normalized conjugacy classes are also shown to belong. A new derivation of such operators based on matrix integrals is proposed, and our vertex operator is used to give an alternative approach to the polynomial functions on Young diagrams introduced by Kerov and Olshanski.

Related

• Vertex algebras and the class algebras of wreath products
• An introduction to the symmetric group algebra
• Vertex operators and sporadic groups
• Representation theory of the vertex algebra W_{1 + ∞}
• Matrix Units in the Symmetric Group Algebra, and Unitary Integration