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- W3102111546 abstract "We study the recently introduced family of confluent Virasoro fusion kernels $mathcal{C}_k(b,boldsymbol{theta},sigma_s,nu)$. We study their eigenfunction properties and show that they can be viewed as non-polynomial generalizations of both the continuous dual $q$-Hahn and the big $q$-Jacobi polynomials. More precisely, we prove that: (i) $mathcal{C}_k$ is a joint eigenfunction of four different difference operators for any positive integer $k$, (ii) $mathcal{C}_k$ degenerates to the continuous dual $q$-Hahn polynomials when $nu$ is suitably discretized, and (iii) $mathcal{C}_k$ degenerates to the big $q$-Jacobi polynomials when $sigma_s$ is suitably discretized. These observations lead us to propose the existence of a non-polynomial generalization of the $q$-Askey scheme. The top member of this non-polynomial scheme is the Virasoro fusion kernel (or, equivalently, Ruijsenaars' hypergeometric function), and its first confluence is given by the $mathcal{C}_k$." @default.
- W3102111546 created "2020-11-23" @default.
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- W3102111546 date "2021-01-01" @default.
- W3102111546 modified "2023-10-18" @default.
- W3102111546 title "The family of confluent Virasoro fusion kernels and a non-polynomial $q$-Askey scheme" @default.
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- W3102111546 doi "https://doi.org/10.4310/atmp.2021.v25.n6.a5" @default.
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