Tokuyama's Identity for Factorial Schur Functions

TL;DR

This paper extends Tokuyama's identity for factorial Schur functions using primed shifted tableaux and non-intersecting lattice paths, providing a broader combinatorial framework for these identities.

Contribution

It generalizes the factorial version of Tokuyama's identity by incorporating primed shifted tableaux and lattice path techniques.

Findings

Extended Tokuyama's identity to factorial Schur functions

Utilized primed shifted tableaux and lattice paths in proof

Provided a combinatorial interpretation of the factorial identity

Abstract

A recent paper of Bump, McNamara and Nakasuji introduced a factorial version of Tokuyama's identity, expressing the partition function of a six vertex model as the product of a t-deformed Vandermonde and a Schur function. Here we provide an extension of their result by exploiting the language of primed shifted tableaux, with its proof based on the use of non-intersecting lattice paths.