Factorization of alternating sums of Virasoro characters

Abstract

G. Andrews proved that if $n$ is a prime number then the coefficients $a_k$ and $a_{k+n}$ of the product $(q,q{)}_{\infty }/(q^n,q^n{)}_{\infty }={\sum }_k{a}_k{q}^k$ have the same sign, see [A1]. We generalize this result in several directions. Our results are based on the observation that many products can be written as alternating sums of characters of Virasoro modules.

Latex, 17 pages. Several formulas and references added

References in corpus (3)

• Fermionic expressions for minimal model Virasoro characters
• Andrews-Gordon identities from combinations of Virasoro characters
• Number theoretic properties of Wronskians of Andrews-Gordon series