scholarly journals Equivariant sheaves on some spherical varieties

2011 ◽  
Vol 18 (0) ◽  
pp. 119-130
Author(s):  
Aravind Asok ◽  
James Parson
Keyword(s):  
Spherical Varieties ◽  
Equivariant Sheaves

scholarly journals Complete intersections in spherical varieties

2016 ◽  
Vol 22 (4) ◽  
pp. 2099-2141 ◽  
Author(s):  
Kiumars Kaveh ◽  
A. G. Khovanskii
Keyword(s):  
Complete Intersections ◽  
Spherical Varieties

scholarly journals Equivariant sheaves

1999 ◽  
Vol 10 (2-3) ◽  
pp. 399-412 ◽  
Author(s):  
Allen Knutson ◽  
Eric Sharpe
Keyword(s):  
Equivariant Sheaves

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

2008 ◽  
Vol 144 (4) ◽  
pp. 978-1016 ◽  
Author(s):  
Yiannis Sakellaridis
Keyword(s):  
Harmonic Analysis ◽  
Weyl Group ◽  
Reductive Group ◽  
Dual Group ◽  
Irreducible Representations ◽  
Spherical Varieties ◽  
Suitable Space ◽  
Borel Orbits ◽  
Left And Right ◽  
New Interpretation

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.

Sign in / Sign up

Export Citation Format

Share Document