A note on corollaries to Tokuyama's Identity for symplectic Schur $Q$-Functions

TL;DR

This paper explores corollaries to Tokuyama's identity for symplectic Schur $Q$-functions, connecting combinatorial objects like shifted tableaux, $U$-turn matrices, and Gelfand-Tsetlin patterns.

Contribution

It introduces new corollaries linking symplectic Schur $Q$-functions with combinatorial constructs, expanding understanding of Tokuyama's identity.

Findings

Derived corollaries relating symplectic Schur $Q$-functions to combinatorial models

Established connections between shifted tableaux and $U$-turn matrices

Enhanced combinatorial interpretations of Tokuyama's identity

Abstract

We present some corollaries to a symplectic primed shifted tableaux version of Tokuyama's identity expressed in terms of other combinatorial constructs, namely generalised $U$-turn alternating sign matrices and strict symplectic Gelfand-Tsetlin patterns.