Reflection for quantum groups and an identity for special functions

Erik Koelink (University of Nijmegen)

Tuesday 30th September, 2014 16:00-17:00 Maths 416

Abstract

Special functions of basic hypergeometric type go back to Euler, Heine, Rogers, Bailey, etc., and have many applications.
With the advent of quantum groups it became clear the quantum groups are the natural `habitat' for many of these
special functions of basic hypergeometric type including both single and multivariable cases.
The interpretation of special functions of basic hypergeometric type on quantum groups is mostly along the lines of the interpretation of
special functions of hypergeometric type on Lie groups, which is many faceted and highly successful in mathematics and applications.
De Commer's recent reflection procedure for quantum groups links two quantum groups using a quantum linking groupoid.
In a special case we discuss the impact on special functions, and in particular we discuss a result coming from this interpretation.
The result can be interpreted as a $q$-analogue of a known result by Arthur Erd\'elyi, who spent
a large part of his career in Scotland. It is remarkable  that
the classical Erd\'elyi result has no group theoretic interpretation.

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