Factorial characters of some classical Lie groups

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.