Hecke Modules from Metaplectic Ice
Representation Theory
2017-10-20 v2 Number Theory
Abstract
We present a new framework for a broad class of affine Hecke algebra modules, and show that such modules arise in a number of settings involving representations of -adic groups and -matrices for quantum groups. Instances of such modules arise from (possibly non-unique) functionals on -adic groups and their metaplectic covers, such as the Whittaker functionals. As a byproduct, we obtain new, algebraic proofs of a number of results concerning metaplectic Whittaker functions. These are thus expressed in terms of metaplectic versions of Demazure operators, which are built out of -matrices of quantum groups depending on the cover degree and associated root system.
Cite
@article{arxiv.1704.00701,
title = {Hecke Modules from Metaplectic Ice},
author = {Ben Brubaker and Valentin Buciumas and Daniel Bump and Solomon Friedberg},
journal= {arXiv preprint arXiv:1704.00701},
year = {2017}
}