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Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures

open access: yes, 2014
We prove two identities of Hall-Littlewood polynomials, which appeared recently in a paper by two of the authors. We also conjecture, and in some cases prove, new identities which relate infinite sums of symmetric polynomials and partition functions ...
Betea, D., Wheeler, M., Zinn-Justin, P.
core   +1 more source

A simple proof of Koornwinder’s addition formula for the little 𝑞-Legendre polynomials [PDF]

open access: yesProceedings of the American Mathematical Society, 1989
Recently Koornwinder found an addition formula for the little q q -Legendre polynomials by using Masuda et al.’s result that they are related to the matrix elements of the irreducible unitary representation of the twisted SU(2) {\text {SU(2)}} quantum group.
openaire   +1 more source

Spherical transform and Jacobi polynomials on root systems of type BC

open access: yes, 2005
Let $R$ be a root system of type BC in $\mathfrak a=\mathbb R^r$ of general positive multiplicity. We introduce certain canonical weight function on $\mathbb R^r$ which in the case of symmetric domains corresponds to the integral kernel of the Berezin ...
Zhang, Genkai
core  

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