Hecke modules from metaplectic ice

Ben Brubaker, Valentin Buciumas, Daniel Bump, Solomon Friedberg

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 p-adic groups and R-matrices for quantum groups. Instances of such modules arise from (possibly non-unique) functionals on p-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 R-matrices of quantum groups depending on the cover degree and associated root system.

Original languageEnglish (US)
Pages (from-to)2523-2570
Number of pages48
JournalSelecta Mathematica, New Series
Volume24
Issue number3
DOIs
StatePublished - Jul 1 2018

Bibliographical note

Funding Information:
Acknowledgements This work was supported by NSF grants DMS-1406238 (Brubaker), DMS-1601026 (Bump), and DMS-1500977 (Friedberg) and by the Max Planck Institute for Mathematics (Buciumas). We would like to thank Sergey Lysenko and Anna Puskás for useful conversations, and the referee for helpful comments.

Keywords

  • Hecke algebra
  • Metaplectic group
  • Quantum group
  • R-matrix
  • Whittaker function

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