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Fundamenta Informaticae
Article . 2012 . Peer-reviewed
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Article . 2012
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Half-lattice Paths and Virasoro Characters

Half-lattice paths and Virasoro characters
Authors: Olivier Blondeau-Fournier; Pierre Mathieu; Trevor A. Welsh;

Half-lattice Paths and Virasoro Characters

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 χp,2p±11,2 that differ from those obtained from the RSOS paths. This work is based on that presented by the third author at the “7th International Conference on Lattice Path Combinatorics and Applications”, Siena, Italy, July 2010.

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Keywords

Permutations, words, matrices, 81R10 (Primary), 05A19, 05A15, 82B23, 17B68 (Secondary), Virasoro and related algebras, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, FOS: Physical sciences, Mathematical Physics (math-ph), \(q\)-calculus and related topics, fermionic expressions, FOS: Mathematics, Mathematics - Combinatorics, Virasoro Lie algebra, Combinatorics (math.CO), Mathematical Physics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
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bronze
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