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Factorial characters and Tokuyama's identity for classical groups

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we introduce factorial characters for the classical groups and derive a number of central results. Classically, the factorial Schur function plays a fundamental role in traditional symmetric function theory and also in Schubert polynomial theory. Here we develop a parallel theory for the classical groups, offering combinatorial definitions of the factorial characters for the symplectic and orthogonal groups, and further proving flagged factorial Jacob-Trudi identities and factorial Tokuyama identities. These identities are established by manipulating determinants through the use of certain recurrence relations and by using lattice paths. This work is joint with Ron King.

Mathematics; Number theory; Quantum theory

video/mp4

Author affiliation: Wilfrid Laurier University

2017-02-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60427

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/