Motivic Springer theory

Motivic Springer theory

We show that representations of convolution algebras such as Lustzig’s graded affine Hecke algebra or the quiver Hecke algebra and quiver Schur algebra in type A and A˜ can be realized in terms of certain equivariant motivic sheaves called Springer motives. To this end, we lay foundations to a motiv...

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Bibliographic Details
Published in:Indagationes mathematicae 2022-01, Vol.33 (1), p.190-217
Main Authors: Eberhardt, Jens Niklas, Stroppel, Catharina
Format: Article
Language:eng
Subjects:
Convolution algebras
Motives
Representation theory
Springer resolution
Weight structures
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Summary:We show that representations of convolution algebras such as Lustzig’s graded affine Hecke algebra or the quiver Hecke algebra and quiver Schur algebra in type A and A˜ can be realized in terms of certain equivariant motivic sheaves called Springer motives. To this end, we lay foundations to a motivic Springer theory and prove formality results using weight structures. As byproduct, we express Koszul and Ringel duality in terms of a weight complex functor and show that partial quiver flag varieties in type A˜ (with cyclic orientation) admit an affine paving.
ISSN:0019-3577
1872-6100