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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 25, Issue 6


The connection problem associated with a Selberg type integral and the q-Racah polynomials

Katsuhisa Mimachi
Published Online: 2011-06-20 | DOI: https://doi.org/10.1515/form.2011.139


The connection problem associated with a Selberg type integral is solved. The connection coefficients are given in terms of the q-Racah polynomials. As an application of the explicit expression of the connection coefficients, examples of the monodromy-invariant Hermitian form of non-diagonal type are presented. It is noteworthy that such Hermitian forms are intimately related with the correlation functions of non-diagonal type in -conformal field theory.

Keywords: Selberg type integral; connection problem; connection coefficient; q-Racah polynomial; twisted homology; monodromy-invariant Hermitian form; conformal field theory; correlation functions of non-diagonal type

About the article

Received: 2010-09-23

Revised: 2011-02-18

Published Online: 2011-06-20

Published in Print: 2013-11-01

Citation Information: Forum Mathematicum, Volume 25, Issue 6, Pages 1127–1179, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.139.

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© 2013 by Walter de Gruyter Berlin Boston.Get Permission

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