Hecke modules from metaplectic ice

• Ben Brubaker ^[1] ; Valentin Buciumas ^[2] ; Daniel Bump ^[3] ; Solomon Friedberg ^[4]
  1. [1] University of Minnesota

     University of Minnesota

     City of Minneapolis, Estados Unidos

     
  2. [2] Hebrew University of Jerusalem

     Hebrew University of Jerusalem

     Israel

     
  3. [3] Stanford University

     Stanford University

     Estados Unidos

     
  4. [4] Boston College

     Boston College

     City of Boston, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 3, 2018, págs. 2523-2570
• Idioma: inglés
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• Resumen

  • 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.