Connection coefficients for basic Harish-Chandra series

Basic Harish-Chandra series are asymptotically free meromorphic solutions of the system of basic hypergeometric difference equations associated to root systems. The associated connection coefficients are explicitly computed in terms of Jacobi theta functions. We interpret the connection coefficients...

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Veröffentlicht in:Advances in mathematics (New York. 1965) Jg. 250; S. 351 - 386
1. Verfasser: Stokman, Jasper V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.01.2014
Schlagworte:
Basic Harish-Chandra series
Basic hypergeometric difference equations
Connection coefficients
Multivariable basic hypergeometric functions
Quantum Knizhnik–Zamolodchikov equations
Connection coefficients
33D67
Basic Harish-Chandra series
Basic hypergeometric difference equations
33D52
Multivariable basic hypergeometric functions
Quantum Knizhnik–Zamolodchikov equations
ISSN:0001-8708, 1090-2082
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Zusammenfassung:Basic Harish-Chandra series are asymptotically free meromorphic solutions of the system of basic hypergeometric difference equations associated to root systems. The associated connection coefficients are explicitly computed in terms of Jacobi theta functions. We interpret the connection coefficients as the transition functions for asymptotically free meromorphic solutions of Cherednikʼs root system analogs of the quantum Knizhnik–Zamolodchikov equations. They thus give rise to explicit elliptic solutions of root system analogs of dynamical Yang–Baxter and reflection equations. Applications to quantum c-functions, basic hypergeometric functions, reflectionless difference operators and multivariable Baker–Akhiezer functions are discussed.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2013.09.016