A Classical Limit of Noumi's $q$-Integral Operator

Abstract

We demonstrate how a known Whittaker function integral identity arises from the $t=0$ and $q\to 1$ limit of the Macdonald polynomial eigenrelation satisfied by Noumi's $q$-integral operator.

References in corpus (4)

• Geometric RSK correspondence, Whittaker functions and symmetrized random polymers
• Baxter operator and Archimedean Hecke algebra
• An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type $A$
• Archimedean zeta integrals on $G{L}_n\times G{L}_m$ and $S{O}_{2n+1}\times G{L}_m$

Cited by in corpus (1)

• An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type $A$