Tuesday, February 8 (2011), at 1:55pm
PLACE: LIT 368
Kenneth I. Gross (University of Vermont)
An Introduction to Special Functions of Matrix Argument
Classical special functions such as the
gamma function, Bessel functions, and hypergeometric functions, to
name a few, apply in many different contexts ranging from
mathematical analysis to statistics and the physical sciences.
Beginning over six decades ago, generalizations of such classical
functions to spaces of matrices, and more generally to symmetric
cones, arose in the context of harmonic analysis, multivariate
statistics, number theory, and the representation theory of Lie
groups. In this talk, expository in nature, we will discuss the
origins of these generalizations, highlight the critical role of
symmetry considerations, and describe some of the applications.