Half-lattice paths and Virasoro characters

DOI10.3233/FI-2012-688zbMATH Open1246.05019arXiv1109.0578OpenAlexW1734288811MaRDI QIDQ2898446

Trevor A. Welsh, Pierre Mathieu, Olivier Blondeau-Fournier

Publication date: 11 July 2012

Published in: Fundamenta Informaticae (Search for Journal in Brave)

Abstract: We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p,p') minimal model characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the M(p,2p+/-1) characters, reformulating them in such a way that the two cases may be treated uniformly. That the generating functions of these half-lattice paths are indeed M(p,2p+/-1) characters is proved by describing weight preserving bijections between them and the corresponding RSOS lattice paths. Here, the M(p,2p-1) case is derived for the first time. We then apply the methods of Bressoud and Warnaar to these half-lattice paths to derive fermionic expressions for the Virasoro characters X^{p,2p+/-1}_{1,2} that differ from those obtained from the RSOS paths. This work is an extension of that presented by the third author at the "7th International Conference on Lattice Path Combinatorics and Applications", Siena, Italy, July 2010.

Full work available at URL: https://arxiv.org/abs/1109.0578

zbMATH Keywords

Virasoro Lie algebra fermionic expressions

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Permutations, words, matrices (05A05) Virasoro and related algebras (17B68) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)