Tokuyama's Formula — Combinatorics of Deformed Schur Polynomials

Okay, there is a cute combinatorial formula for a deformation of the Schur polynomial. The deformation behaves fantastically: the formula generalizes Gelfand's parametrization, Jacobi's bialternant formula, and Stanley's Formula on Hall-Littlewood polynomials. Moreover, the arising combinatorics is identical to combinatorics of alternating sign matrices and six-vertex lattice models. In the end, I will explain why everything works so well (spoiler: representations of p-adic groups!). The talk is based on my recent post on Thuses. (https://thuses.com/combinatorics/simple-proof-of-tokuyamas-formula/).