Sklyanin Invariant Integration
نویسنده
چکیده
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.
منابع مشابه
Vacuum curves of elliptic L-operators and representations of Sklyanin algebra
An algebro-geometric approach to representations of Sklyanin algebra is proposed. To each 2×2 quantum L-operator an algebraic curve parametrizing its possible vacuum states is associated. This curve is called the vacuum curve of the L-operator. An explicit description of the vacuum curve for quantum L-operators of the integrable spin chain of XY Z type with arbitrary spin l is given. The curve ...
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This note being devoted to some aspects of the inverse problem of representation theory explicates the links between researches on the Sklyanin algebras and the author’s (based on the noncommutative geometry) approach to the setting free of hidden symmetries in terms of ”the quantization of constants”. Namely, the Racah–Wigner algebra for the Sklyanin algebra is constructed. It may be considere...
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