Showing papers by "Kirill Zainoulline published in 2018"
TL;DR: In this article, a uniform de-scription of motivic decompositions with integer coefficients of flag varieties in terms of integer representations of the associated affine nil-Hecke algebra H is provided.
9 citations
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TL;DR: In this article, the authors studied twisted foldings of root systems which generalize usual involutive foldings corresponding to automorphisms of Dynkin diagrams and constructed a map at the equivariant cohomology level.
Abstract: In the present paper we study twisted foldings of root systems which generalize usual involutive foldings corresponding to automorphisms of Dynkin diagrams. Our motivating example is the Lusztig projection of the root system of type $E_8$ onto the subring of icosians of the quaternion algebra which gives the root system of type $H_4$.
Using moment graph techniques for any such folding we construct a map at the equivariant cohomology level. We show that this map commutes with characteristic classes and Borel maps. We also introduce and study its restrictions to the usual cohomology of projective homogeneous varieties, to group cohomology and to their virtual analogues for finite reflection groups.
8 citations