Vertex algebras and the class algebras of wreath products
| dc.creator | Wang, Weiqiang | |
| dc.date | 2002-02-28 | |
| dc.date | 2003-02-18 | |
| dc.date.accessioned | 2026-07-07T04:46:46Z | |
| dc.date.available | 2026-07-07T04:46:46Z | |
| dc.description | The Jucys-Murphy elements for wreath products G_n associated to any finite group G are introduced and they play an important role in our study on the connections between class algebras of G_n for all n and vertex algebras. We construct an action of (a variant of) the W_{1+\infty} algebra acting irreducibly on the direct sum R_G of the class algebras of G_n for all n in a group theoretic manner. We establish various relations between convolution operators using JM elements and Heisenberg algebra operators acting on R_G. As applications, we obtain two distinct sets of algebra generators for the class algebra of G_n and establish various stability results concerning products of normalized conjugacy classes of G_n and the power sums of Jucys-Murphy elements etc. We introduce a stable algebra which encodes the class algebra structures of G_n for all n, whose structure constants are shown to be non-negative integers. In the symmetric group case (i.e. G is trivial), we recover and strengthen in a uniform approach various results of Lascoux-Thibon, Kerov-Olshanski, and Farahat-Higman, etc. | |
| dc.description | 25 pages, latex, minor changes, to appear in Proc. London Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0203004 | |
| dc.identifier | http://arxiv.org/abs/math/0203004 | |
| dc.identifier | Proc. London Math. Soc. 88 (2004), 381--404. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63464 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | Vertex algebras and the class algebras of wreath products | |
| dc.type | text |