The Parabolic K-motivic Hecke Category
Representation Theory
2025-11-26 v1 Algebraic Geometry
K-Theory and Homology
Abstract
We define and study the parabolic K-motivic Hecke category of a (possibly disconnected) Kac-Moody group. Our main result is a combinatorial description via singular K-theory Soergel bimodules which arise from the equivariant algebraic K-theory of parabolic Bott-Samelson resolutions. In the spherical affine case, the K-motivic Hecke category serves as one side of a conjectural quantum K-theoretic derived Satake equivalence, addressing a conjecture of Cautis-Kamnitzer.
Keywords
Cite
@article{arxiv.2511.19618,
title = {The Parabolic K-motivic Hecke Category},
author = {Jens Niklas Eberhardt and Arnaud Eteve},
journal= {arXiv preprint arXiv:2511.19618},
year = {2025}
}