Categorical diagonalization of full twists
Representation Theory
2025-05-02 v2 Geometric Topology
Quantum Algebra
Abstract
We conjecture that the complex of Soergel bimodules associated with the full twist braid is categorically diagonalizable, for any finite Coxeter group. This utilizes the theory of categorical diagonalization introduced earlier by the authors. We prove our conjecture in type , and as a result we obtain a categorification of the Young idempotents.
Cite
@article{arxiv.1801.00191,
title = {Categorical diagonalization of full twists},
author = {Ben Elias and Matthew Hogancamp},
journal= {arXiv preprint arXiv:1801.00191},
year = {2025}
}