Colored vertex models and Iwahori Whittaker functions

• Ben Brubaker ^[1] ; Valentin Buciumas ^[2] ; Daniel Bump ^[3] ; Henrik P. A. Gustafsson ^[3]
  1. [1] University of Minnesota

     University of Minnesota

     City of Minneapolis, Estados Unidos

     
  2. [2] Pohang University of Science and Technology

     Pohang University of Science and Technology

     Corea del Sur

     
  3. [3] Stanford University

     Stanford University

     Estados Unidos

     

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 4, 2024, págs. 1-58
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.