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Algebra Seminar
University of Sydney> Maths & Stats> Research> Algebra Seminar> Abstracts


Xiaoping Xu
Institute of Mathematics, Chinese Academy of Sciences

Path hypergeometric functions and representations of gl(n)

Friday 18th June, 12:05-12:55pm, Carslaw 373.

Trace functions of intertwining operators among gl(n)-modules were introduced by Etingof in connection with the solutions of the Calogero-Sutherland model. We find the explicit formulae for trace functions under certain conditions. If n=2, the master function of the trace function is exactly the classical Gauss hypergeometric function. When n>2, the master functions of the trace functions are a new family of multiple hypergeometric functions, whose differential property and integral representation are determined by some polynomials associated with integral paths connecting pairs of positive integers.