Motivic Springer Theory

Jens Niklas Eberhardt; Catharina Stroppel

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arXiv · 2109.00305

Motivic Springer Theory

Jens Niklas Eberhardt·Catharina Stroppel

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Abstract

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 (affine) type A can be realised 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 affine type A (with cyclic orientation) admit an affine paving.

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BibTeX RIS

Jens Niklas Eberhardt, Catharina Stroppel. 2021-11-14. Motivic Springer Theory. https://arxiv.org/abs/2109.00305

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