sl3-web bases, intermediate crystal bases and categorification

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  • Daniel Tubbenhauer, Denmark
We give an explicit graded cellular basis of the sl3-web algebra K_S.
In order to do this, we identify Kuperberg's basis for the sl3-web space W_S with a version of Leclerc-Toffin's intermediate crystal basis and we identify Brundan, Kleshchev and Wang's degree of tableaux with the weight of flows on webs and the q-degree of foams.
We use this to give a “foamy” version of Hu and Mathas graded cellular basis of the cyclotomic Hecke algebra which turns out to be a graded cellular basis of the sl3-web algebra K_S.
We restrict ourselves to the sl3 case here, but our approach should, up to the combinatorics of sln-webs, work for all n>1.
Original languageEnglish
JournalJournal of Algebraic Combinatorics
Volume40
Issue4
Pages (from-to)1001-1076
Number of pages76
ISSN0925-9899
DOIs
Publication statusPublished - 20 Feb 2014

    Research areas

  • Categorification, Categorial representation theory, Combinatorial representation theory, Quantum groups, Canonical bases

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