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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Jiang, Dihua Nien, Chufeng and Qin, Yujun 2013. Generalized Shalika models of p-adic SO4n and functoriality. Israel Journal of Mathematics, Vol. 195, Issue. 1, p. 135.


    Sakellaridis, Yiannis 2012. Spherical varieties and integral representations ofL-functions. Algebra & Number Theory, Vol. 6, Issue. 4, p. 611.


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On the unramified spectrum of spherical varieties over p-adic fields

  • Yiannis Sakellaridis (a1)
  • DOI: http://dx.doi.org/10.1112/S0010437X08003485
  • Published online: 01 July 2008
Abstract
Abstract

The description of irreducible representations of a group G can be seen as a problem in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G×G by left and right multiplication. For a split p-adic reductive group G over a local non-archimedean field, unramified irreducible smooth representations are in bijection with semisimple conjugacy classes in the ‘Langlands dual’ group. We generalize this description to an arbitrary spherical variety X of G as follows. Irreducible unramified quotients of the space are in natural ‘almost bijection’ with a number of copies of AX*/WX, the quotient of a complex torus by the ‘little Weyl group’ of X. This leads to a description of the Hecke module of unramified vectors (a weak analog of geometric results of Gaitsgory and Nadler), and an understanding of the phenomenon that representations ‘distinguished’ by certain subgroups are functorial lifts. In the course of the proof, rationality properties of spherical varieties are examined and a new interpretation is given for the action, defined by Knop, of the Weyl group on the set of Borel orbits.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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