Sklyanin invariant integration

Details Sklyanin invariant integration Sklyanin invariant integration

Publishing date

2004-05-05

URL

arxiv.org/abs/math/0405072v1

Journals

Int. Math. Res. Not. 2004 (2004), 3207-3232

Science

Mathematics

Field

Quantum Algebra

Additional info

21 pages

Type

Scientific paper

Abstract

The Sklyanin algebra admits realizations by difference operators acting on theta functions. Sklyanin found an invariant metric for the action and conjectured an explicit formula for the corresponding reproducing kernel. We prove this conjecture, and also give natural biorthogonal and orthogonal bases for the representation space. Moreover, we discuss connections with elliptic hypergeometric series and integrals and with elliptic 6j-symbols.

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