Bibliographic Details
| Title: |
K‐theory Soergel bimodules. |
| Authors: |
Eberhardt, Jens Niklas1 (AUTHOR) mail@jenseberhardt.com |
| Superior Title: |
Bulletin of the London Mathematical Society. Mar2024, Vol. 56 Issue 3, p1169-1191. 23p. |
| Subject Terms: |
*K-theory, *LOGICAL prediction |
| Abstract: |
We initiate the study of K$K$‐theory Soergel bimodules, a global and K$K$‐theoretic version of Soergel bimodules. We show that morphisms of K$K$‐theory Soergel bimodules can be described geometrically in terms of equivariant K$K$‐theoretic correspondences between Bott–Samelson varieties. We thereby obtain a natural categorification of K$K$‐theory Soergel bimodules in terms of equivariant coherent sheaves. We introduce a formalism of stratified equivariant K$K$‐motives on varieties with an affine stratification, which is a K$K$‐theoretic analog of the equivariant derived category of Bernstein–Lunts. We show that Bruhat‐stratified torus‐equivariant K$K$‐motives on flag varieties can be described in terms of chain complexes of K$K$‐theory Soergel bimodules. Moreover, we propose conjectures regarding an equivariant/monodromic Koszul duality for flag varieties and the quantum K$K$‐theoretic Satake. [ABSTRACT FROM AUTHOR] |
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| Database: |
Academic Search Premier |
