Cellularity of KLR and weighted KLRW algebras via crystals

Autor:	Mathas, Andrew, Tubbenhauer, Daniel
Rok vydání:	2023
Předmět:	Mathematics - Representation Theory Mathematics - Combinatorics Mathematics - Rings and Algebras Primary 18M30 20C08 Secondary 05E10 17B10 18N25
Druh dokumentu:	Working Paper
Popis:	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. Comment: 54 pages, many figures, updated version, comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.13867 Zobrazit plný text záznamu View this record from Arxiv