Cuspidal hypergeometric functions

Details Cuspidal hypergeometric functions Cuspidal hypergeometric functions

1998-08-06

arxiv.org/abs/math/9808035v1

Mathematics

Representation Theory

18 pages, no figures. This paper is dedicated to Richard Askey, on the occasion of his 65th birthday. It will appear in a spec

Scientific paper

We prove the Plancherel formula for hypergeometric functions associated to a
root system in the situation when the root multiplicities are negative (but
close to 0). As a result we obtain a classification of the hypergeometric
functions that are square integrable, and we find a closed formula for their
square norm as a function of the root multiplicities.

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