2025/09/22 by Ben Brubaker, Brubaker, Ben, Daniel Bump +5
Mathematics · #05E14 #14C17 #14M15 #16T25 #22E50 #82B23 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2509.17312
openalex publication_date 2025/09/22 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
We will describe solvable lattice models whose partition functions depend on two sets of variables, x1,⋯,xn and y1, y2, ⋯ that have different connections with the representation theory of GL(n,F) where F is a nonarchimedean local field. If the boundary conditions are chosen in one way, they are essentially the Motivic Chern classes that were used very effectively by Aluffi, Mihalcea, Schürmann and Su (AMSS) to study such problems. In particular, using this specialization we can obtain deformations ru,v of the Kazhdan-Lusztig R-polynomials that were used by Bump, Nakasuji and Naruse to study matrix coefficients of intertwining operators (introduced by Casselman). Thus we are able see that the recursion formula for the ru,v is a reflection of the Yang-Baxter equation. On the other hand, with more general boundary conditions, specializing the parameters yi→ 0 we recover colored lattice models that were previously used by Brubaker, Buciumas, Bump and Gustafsson to represent Iwahori Whittaker functions on GL(n,F). Thus we term the resulting two-variable-set family of functions as ``double Whittaker polynomials.''