pith. sign in

arxiv: 2309.13867 · v3 · pith:7TAG7MU3new · submitted 2023-09-25 · 🧮 math.RT · math.CO· math.RA

Cellularity of KLR and weighted KLRW algebras via crystals

Andrew Mathas , Daniel Tubbenhauer This is my paper
classification 🧮 math.RT math.COmath.RA
keywords algebrascellularcyclotomicfiniteklrwtypeweightedapplication
0
0 comments X
read the original abstract

We prove that the weighted KLRW algebras of finite type, and their cyclotomic quotients, are cellular algebras. The cellular bases are explicitly described using crystal graphs. As a special case, this proves that the KLR algebras of finite type are cellular. As one application, we give explicit formulas for the graded decomposition numbers of the cyclotomic algebras in level one.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Presentations for categories of crystals

    math.RT 2026-06 unverdicted novelty 5.0

    Provides generators and relations for monoidal crystal categories of simple complex Lie algebras with explicit small-rank examples.