Colored vertex models and Iwahori Whittaker functions
Artikel i vetenskaplig tidskrift, 2024

We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split reductive group G over a nonarchimedean local field F. Structures in the proof have surprising analogies to features of certain solvable lattice models. In the case G=GLr we show that there exist solvable lattice models whose partition functions give precisely all of these values. Here ‘solvable’ means that the models have a family of Yang–Baxter equations which imply, among other things, that their partition functions satisfy the same recursions as those for Iwahori or parahoric Whittaker functions. The R-matrices for these Yang–Baxter equations come from a Drinfeld twist of the quantum group Uq(gl^(r|1)), which we then connect to the standard intertwining operators on the unramified principal series. We use our results to connect Iwahori and parahoric Whittaker functions to variations of Macdonald polynomials.

16T25

Quantum group

05E05

Primary 22E50

Parahoric Whittaker function

Demazure operator

82B23

Yang–Baxter equation

Macdonald polynomial

Whittaker function

Secondary 11F70

Iwahori Whittaker function

Solvable lattice model

Författare

Ben Brubaker

University of Minnesota

Valentin Buciumas

Pohang University of Science and Technology

Daniel Bump

Stanford University

Henrik Gustafsson

Umeå universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Institute for Advanced Studies

Rutgers University

Stanford University

Selecta Mathematica, New Series

1022-1824 (ISSN) 14209020 (eISSN)

Vol. 30 4 78

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1007/s00029-024-00950-6

Mer information

Senast uppdaterat

2024-09-18