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Addition formula for q-disk polynomials

Published online by Cambridge University Press:  04 December 2007

PAUL G. A. FLORIS
PAUL G. A. FLORIS
Affiliation:
University of Leiden, Department of Mathematics and Computer Science, P.O. Box 9512, 2300 RA Leiden, The Netherlands; e-mail: floriswi.leidenuniv.nl
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Abstract

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Abstract. Explicit models are constructed for irreducible *-representations of the quantised universal enveloping algebra $U_q({\frak g}{\frak l}(n))$. The irreducible decomposition of these modules with respect to the subalgebra $U_q({\frak g}{\frak l}(n-1))$ is given, and the corresponding spherical and associated spherical elements are determined in terms of little $q$-Jacobi polynomials. This leads to a proof of an addition theorem for the spherical elements, the so-called $q$-disk polynomials.

Keywords

CQG algebrasquantum unitary groupquantized universal enveloping algebraspherical elements$q$-disk polynomialsaddition formula
Type
Research Article
Information
Compositio Mathematica , Volume 108 , Issue 2 , September 1997 , pp. 123 - 149
Copyright
© 1997 Kluwer Academic Publishers