Elliptic U(2) quantum group and elliptic hypergeometric series

Details Elliptic U(2) quantum group and elliptic hypergeometric series Elliptic U(2) quantum group and elliptic hypergeometric series

2003-04-15

arxiv.org/abs/math/0304189v1

Communications in Mathematical Physics 245 (2004), 519-537

Mathematics

Quantum Algebra

20 pages

Scientific paper

10.1007/s00220-003-1016-0

We investigate an elliptic quantum group introduced by Felder and Varchenko, which is constructed from the $R$-matrix of the Andrews-Baxter-Forrester model, containing both spectral and dynamical parameter. We explicitly compute the matrix elements of certain corepresentations and obtain orthogonality relations for these elements. Using dynamical representations these orthogonality relations give discrete bi-orthogonality relations for terminating very-well-poised balanced elliptic hypergeometric series, previously obtained by Frenkel and Turaev and by Spiridonov and Zhedanov in different contexts.

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