Hecke modules from metaplectic ice

Ben Brubaker, Valentin Buciumas, Daniel Bump, Solomon Friedberg

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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
Issue number3
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.


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

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