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Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras.
- Source :
-
Advances in Mathematics . Dec2018, Vol. 340, p791-818. 28p. - Publication Year :
- 2018
-
Abstract
- Abstract Let G be a split semisimple linear algebraic group over a field k 0. Let E be a G -torsor over a field extension k of k 0. Let h be an algebraic oriented cohomology theory in the sense of Levine–Morel. Consider a twisted form E / B of the variety of Borel subgroups G / B over k. Following the Kostant–Kumar results on equivariant cohomology of flag varieties we establish an isomorphism between the Grothendieck groups of the h-motivic subcategory generated by E / B and the category of finitely generated projective modules of certain Hecke-type algebra H which depends on the root datum of G , on the torsor E and on the formal group law of the theory h. In particular, taking h to be the Chow groups with finite coefficients F p and E to be a generic G -torsor we prove that all finitely generated projective indecomposable submodules of an affine nil-Hecke algebra H of G with coefficients in F p are isomorphic to each other and correspond to the (non-graded) generalized Rost–Voevodsky motive for (G , p). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 340
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 132868575
- Full Text :
- https://doi.org/10.1016/j.aim.2018.10.014