Trace decategorification of the Hecke category

TL;DR

This paper introduces a new framework called strictly object-adapted cellular categories and computes the trace decategorification of the Hecke category for any Coxeter group, advancing understanding of categorical structures.

Contribution

It defines strictly object-adapted cellular categories and calculates their trace, extending trace decategorification to the Hecke category for all Coxeter groups.

Findings

Computed the trace decategorification for the Hecke category of any Coxeter group.

Introduced the concept of strictly object-adapted cellular categories.

Extended trace decategorification techniques to new categorical structures.

Abstract

We compute the trace decategorification of the Hecke category for an arbitrary Coxeter group. More generally, we introduce the notion of a strictly object-adapted cellular category and calculate the trace for such categories.