Abstract: Schur polynomials and their generalizations appear in various different contexts. They are the irreducible characters of polynomial representations of the general linear group and an important basis of the space of symmetric functions. They are accessible from a combinatorial point of view as they are multivariate generating functions of semistandard tableaux of a fixed integer partition. Recently, Ayyer and Behrend discovered certain factorizations of Schur polynomials with an even number of variables where half of the variables are the reciprocals of the others into symplectic and/or orthogonal group characters. This generalizes results of Ciucu and Krattenthaler for rectangular shapes. We present bijective proofs of such identities. Our proofs involve what we call a ``randomized'' bijection.

This is joint work with Arvind Ayyer.

Zoom-Meeting beitreten: zoom.us/j/95266898496
Meeting-ID: 952 6689 8496
Kenncode: p291Sc