K-theoretic wall-crossing formulas and multiple basic hypergeometric series

We study K-theoretic integrals over framed quiver moduli via wall-crossing phenomena. We study the chainsaw quiver varieties, and consider generating functions defined by two types of K-theoretic classes. In particular, we focus on integrals over the handsaw quiver varieties of type A1, and get func...

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Veröffentlicht in:Journal of algebra Jg. 677; S. 516 - 584
Hauptverfasser: Ohkawa, R., Shiraishi, J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.09.2025
Schlagworte:
Affine Laumon function
Chainsaw quiver variety
Framed quiver moduli
Handsaw quiver variety
Kajihara transformation
Multiple basic hypergeometric series
Non-stationary Ruijsenaars function
Wall-crossing formula
Affine Laumon function
Handsaw quiver variety
Framed quiver moduli
Multiple basic hypergeometric series
Kajihara transformation
Wall-crossing formula
Chainsaw quiver variety
Non-stationary Ruijsenaars function
ISSN:0021-8693
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Zusammenfassung:We study K-theoretic integrals over framed quiver moduli via wall-crossing phenomena. We study the chainsaw quiver varieties, and consider generating functions defined by two types of K-theoretic classes. In particular, we focus on integrals over the handsaw quiver varieties of type A1, and get functional equations for each of them. We also give explicit formula for these partition functions. In particular, we obtain geometric interpretation of transformation formulas for multiple basic hypergeometric series including the Kajihara transformation formula, and the one studied by Langer-Schlosser-Warnaar and Hallnäs-Langman-Noumi-Rosengren.
ISSN:0021-8693
DOI:10.1016/j.jalgebra.2025.03.042