Factorial characters of some classical Lie groups

TL;DR

This paper introduces factorial characters for classical Lie groups, establishes flagged Jacobi-Trudi identities, and provides combinatorial formulas using lattice paths and tableaux, including factorial Q-functions with Tokuyama identities.

Contribution

It defines factorial characters for classical Lie groups and derives combinatorial and algebraic identities connecting them to tableaux and lattice path models.

Findings

Factorial characters satisfy flagged Jacobi-Trudi identities.

Combinatorial expressions are given via lattice paths and tableaux.

Factorial Q-functions obey Tokuyama type identities.

Abstract

A definition is offered of the factorial characters of the general linear group, the symplectic group and the orthogonal group in an odd dimensional space. It is shown that these characters satisfy certain flagged Jacobi-Trudi identities. These identities are then used to give combinatorial expressions for the factorial characters: first in terms of a lattice path model and then in terms of the well known tableaux associated with the classical groups. Factorial Q-functions are then defined in terms of three sets of primed shifted tableaux, and shown to satisfy Tokuyama type identities in each case.