Author:
Brubaker Ben,Buciumas Valentin,Bump Daniel,Gustafsson Henrik P. A.
Abstract
AbstractWe 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 $$G=\textrm{GL}_r$$
G
=
GL
r
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 $$U_q(\widehat{\mathfrak {gl}}(r|1))$$
U
q
(
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.
Publisher
Springer Science and Business Media LLC
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