K-theory Soergel Bimodules
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914686583177216 |
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| author | Eberhardt, Jens Niklas |
| author_facet | Eberhardt, Jens Niklas |
| contents | We initiate the study of K-theory Soergel bimodules-a K-theory analog of classical Soergel bimodules. Classical Soergel bimodules can be seen as a completed and infinitesimal version of their new K-theoretic analog. We show that morphisms of K-theory Soergel bimodules can be described geometrically in terms of equivariant K-theoretic correspondences between Bott-Samelson varieties. We thereby obtain a natural categorification of K-theory Soergel bimodules in terms of equivariant coherent sheaves. We introduce a formalism of stratified equivariant K-motives on varieties with an affine stratification, which is a K-theoretric analog of the equivariant derived category of Bernstein-Lunts. We show that Bruhat-stratified torus-equivariant K-motives on flag varieties can be described in terms of chain complexes of K-theory Soergel bimodules. Moreover, we propose conjectures regarding an equivariant/monodromic Koszul duality for flag varieties and the quantum K-theoretic Satake. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_01665 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | K-theory Soergel Bimodules Eberhardt, Jens Niklas Representation Theory K-Theory and Homology We initiate the study of K-theory Soergel bimodules-a K-theory analog of classical Soergel bimodules. Classical Soergel bimodules can be seen as a completed and infinitesimal version of their new K-theoretic analog. We show that morphisms of K-theory Soergel bimodules can be described geometrically in terms of equivariant K-theoretic correspondences between Bott-Samelson varieties. We thereby obtain a natural categorification of K-theory Soergel bimodules in terms of equivariant coherent sheaves. We introduce a formalism of stratified equivariant K-motives on varieties with an affine stratification, which is a K-theoretric analog of the equivariant derived category of Bernstein-Lunts. We show that Bruhat-stratified torus-equivariant K-motives on flag varieties can be described in terms of chain complexes of K-theory Soergel bimodules. Moreover, we propose conjectures regarding an equivariant/monodromic Koszul duality for flag varieties and the quantum K-theoretic Satake. |
| title | K-theory Soergel Bimodules |
| topic | Representation Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2208.01665 |