The singular support of the Ising model

2020/05/21 by Andrews, George E., van Ekeren, Jethro, Heluani, Reimundo · 3 citations
#11P84 #17B69 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2005.10769

Abstract

We prove a new Fermionic quasiparticle sum expression for the character of the Ising model vertex algebra, related to the Jackson-Slater q-series identity of Rogers-Ramanujan type and to Nahm sums for the matrix ( \beginsmallmatrix 8 & 3 3 & 2 \endsmallmatrix ). We find, as consequences, an explicit monomial basis for the Ising model, and a description of its singular support. We find that the ideal sheaf of the latter, defining it as a subscheme of the arc space of its associated scheme, is finitely generated as a differential ideal. We prove three new q-series identities of the Rogers-Ramanujan-Slater type associated with the three irreducible modules of the Virasoro Lie algebra of central charge 1/2. We give a combinatorial interpretation to the identity associated with the vacuum module.

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• Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules
• Leading terms of relations on a level 5 module over the twisted affine Lie algebra A₂⁽²⁾
• Associated Varieties of Ordinary Modules over Quasi-Lisse Vertex Algebras

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