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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Bibliographic Details
Published in:	Journal of algebra Vol. 677; pp. 516 - 584
Main Authors:	Ohkawa, R., Shiraishi, J.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.09.2025
Subjects:	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
Online Access:	Get full text
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Summary:	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