Alex Molev (University of Sydney)

Friday 23rd May, 12.05-12.55pm, Carslaw 373

Cauchy identity for double Schur functions and its applications

The double (or factorial) analogues of the Schur functions turned out to have useful applications in the geometry of Grassmannians and in representation theory. We establish new properties of these functions by proving an analogue of the Cauchy identity. This leads to a construction of natural bases of the ring of double symmetric functions and to formulas for the irreducible characters of the symmetric group.