scholarly journals EQUIVARIANT MODELS OF SPHERICAL VARIETIES

2019 ◽  
Vol 25 (2) ◽  
pp. 391-439 ◽  
Author(s):  
MIKHAIL BOROVOI
Keyword(s):  
2016 ◽  
Vol 22 (4) ◽  
pp. 2099-2141 ◽  
Author(s):  
Kiumars Kaveh ◽  
A. G. Khovanskii

2008 ◽  
Vol 144 (4) ◽  
pp. 978-1016 ◽  
Author(s):  
Yiannis Sakellaridis

AbstractThe 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 $C_c^\infty (X)$ 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.


2018 ◽  
Vol 328 ◽  
pp. 1299-1352 ◽  
Author(s):  
Roman Avdeev ◽  
Stéphanie Cupit-Foutou

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