Séminaire Lotharingien de Combinatoire, B14c (1986), 38 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1986, 323/S-14, p.
5-42.]
David Bressoud
Constant Term Identities
Abstract.
This article is intended as an overview of a very rapidly developing
and exciting subject. The problem at hand is the evaluation of the
constant term in the Laurent expansions of certain products indexed by
root systems of Lie algebras. These evaluations are equivalent to
computing certain multi-dimenslonal definite integrals which have
arisen in physical problems.
The implications of this subject, however, go far beyond their
physical applications. As will be discussed in the last section, there
are tie-ins to representation theory and the decomposition of
characters, to cyclic homology and most significantly to higher
dimensional analogs of hypergeometric series which carry the symmetry
of the Weyl group of the associated root system.
The following version is available: