Treffer: Sklyanin invariant integration
Title:
Sklyanin invariant integration
Authors:
Source:
International Mathematics Research Notices. 2004(60):3207-3232
Publication Status:
Preprint
Publisher Information:
arXiv, 2004.
Publication Year:
2004
Subject Terms:
11F50, 17B37, 33D80, Quantum groups (quantized enveloping algebras) and related deformations, Connections of hypergeometric functions with groups and algebras, and related topics, 01 natural sciences, elliptic quantum groups, Sklyanin algebra, Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), Discrete version of topics in analysis, 0101 mathematics, Quantum groups and related algebraic methods applied to problems in quantum theory, Exactly solvable models, Bethe ansatz, elliptic \(6j\)-symbols
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
ISSN:
1073-7928
DOI:
10.48550/arxiv.math/0405072
DOI:
10.1155/s1073792804141731
Access URL:
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....7509556d0bd017a4fbe124273bc7910a
Database:
OpenAIRE
Weitere Informationen
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.
21 pages