UTMS 2007 – 4 April 18 , 2007 Harish - Chandra expansion

Macdonald Difference Operators and Harish-chandra Series

We analyze the centralizer of the Macdonald difference operator in an appropriate algebra of Weyl group invariant difference operators. We show that it coincides with Cherednik’s commuting algebra of difference operators via an analog of the Harish-Chandra isomorphism. Analogs of Harish-Chandra series are defined and realized as solutions to the system of basic hypergeometric difference equatio...

Globalizations of Harish-chandra Modules

Correction to Abstract Class Formations by K. Grant and G. Whaples

1. A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Bull. Amer. Math. Soc. 67 (1961), 579-583. 2. , Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485-535. 3. Harish-Chandra, On the characters of a semisimple Lie group, Bull. Amer. Math. Soc. 61 (1955), 389-396. 4. , Differential operators on a semisimple Lie algebra, Amer. J. Math. 79 (1957), 87-12...

Harish-chandra and His Work

I began to study representation theory while I was a graduate student at the University of Washington in the early seventies. At that time learning the theory of unitary representations of semisimple Lie groups primarily meant learning Harish-Chandra's work, and it was not an easy task. By that time Harish-Chandra had published over fifty papers, more than a thousand pages, on this subject. His...

The Cauchy Harish-chandra Integral, for the Pair

One of the main problems in the theory of dual pairs is the description of the correspondence of characters of representations in Howe duality, [H]. In [D-P] a formula describing this correspondence was obtained under some very strong assumptions. In [P] the second author has developed a notion of a Cauchy Harish-Chandra integral for any real reductive pair, in order to describe this correspond...