Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras

Alexander Neshitov, Victor Petrov, Nikita Semenov, Kirill Zainoulline

Результат исследований: Научные публикации в периодических изданияхстатья

1 цитирование (Scopus)

Выдержка

Let G be a split semisimple linear algebraic group over a field k0. Let E be a G-torsor over a field extension k of k0. 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 Fp 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 Fp are isomorphic to each other and correspond to the (non-graded) generalized Rost–Voevodsky motive for (G,p).

Язык оригиналаанглийский
Страницы (с-по)791-818
Число страниц28
ЖурналAdvances in Mathematics
Том340
DOI
СостояниеОпубликовано - 2018

Отпечаток

Torsor
Flag Variety
Decompose
Algebra
Finitely Generated
Formal Group Law
Grothendieck Group
Chow Groups
Linear Algebraic Groups
Equivariant Cohomology
Nil
Projective Module
Hecke Algebra
Field extension
Coefficient
Semisimple
Cohomology
Isomorphism
Isomorphic
Roots

Предметные области Scopus

  • Математика (все)

Цитировать

Neshitov, Alexander ; Petrov, Victor ; Semenov, Nikita ; Zainoulline, Kirill. / Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras. В: Advances in Mathematics. 2018 ; Том 340. стр. 791-818.
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Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras. / Neshitov, Alexander; Petrov, Victor; Semenov, Nikita; Zainoulline, Kirill.

В: Advances in Mathematics, Том 340, 2018, стр. 791-818.

Результат исследований: Научные публикации в периодических изданияхстатья

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