Growth in affine Hecke categories
Asymptotic growth of tensor powers in affine Hecke categories, with precise results in low affine type.
Data
- Title: Growth in affine Hecke categories
- Authors: Kevin Coulembier, Jensen O'Sullivan and Daniel Tubbenhauer
- Status: preprint. Last update: Wed, 29 Apr 2026 02:19:47 GMT
- Code / errata: GitHub
- arXiv: https://arxiv.org/abs/2603.07955
Abstract
This paper studies the asymptotic growth of tensor powers in affine Hecke categories, or equivalently of powers of Kazhdan–Lusztig basis elements in affine Hecke algebras. We prove general bounds in arbitrary affine type, determine precise asymptotics in affine type A1, and several natural families in affine type A2.
What is the point?
Take a basic algebraic object and multiply it with itself again and again. The first few powers are often messy. The long-term behaviour, however, can reveal a clean mixture of exponential growth, polynomial correction terms and geometry. In affine Hecke categories this becomes a concrete growth problem in Kazhdan–Lusztig theory.
affine Hecke category.
take tensor powers.
asymptotic laws and bounds.
A picture
One can think of the affine Weyl group picture as the geometric board on which the asymptotic walk takes place. Joel Gibson's Lievis is very useful for this viewpoint.
