
Xiaoping Xu
Institute of Mathematics,
Chinese Academy of Sciences
Path hypergeometric functions and representations of gl(n)
Friday 18th June, 12:0512:55pm,
Carslaw 373.
Trace functions of intertwining operators among
gl(n)modules were
introduced by Etingof in connection with the
solutions of the CalogeroSutherland 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.







