Factorial [formula omitted]-functions and Tokuyama identities for classical Lie groups

Abstract

Factorial characters of each of the classical Lie groups have recently been defined algebraically as rather simple deformations of irreducible characters. Each such factorial character has been shown to satisfy a flagged Jacobi–Trudi identity, thereby allowing for its combinatorial realisation in terms of first a non-intersecting lattice path model and then a tableau model. Here we propose algebraic definitions of factorial Q-functions of the classical Lie groups and translate these definitions into combinatorial realisations in terms of non-intersecting lattice path and primed shifted tableaux models. By way of some justification of our chosen definitions, it is then shown that our factorial Q-functions satisfy Tokuyama-type identities and relate some special case of these to other identities that have appeared in the literature.