Young walls and graded dimension formulas for finite quiver Hecke algebras of type A(2)2l and D(2)l+1

Se Jin Oh, Euiyong Park

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study graded dimension formulas for finite quiver Hecke algebras RΛ0(β) of type A2ℓ(2) and Dℓ+1(2) using combinatorics of Young walls. We introduce the notion of standard tableaux for proper Young walls and show that the standard tableaux form a graded poset with lattice structure. We next investigate Laurent polynomials associated with proper Young walls and their standard tableaux arising from the Fock space representations consisting of proper Young walls. Then, we prove the graded dimension formulas described in terms of the Laurent polynomials. When evaluating at $$q=1$$q=1, the graded dimension formulas recover the dimension formulas for RΛ0(β) described in terms of standard tableaux of strict partitions.

Original languageEnglish
Pages (from-to)1077-1102
Number of pages26
JournalJournal of Algebraic Combinatorics
Volume40
Issue number4
DOIs
StatePublished - 1 Dec 2014

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

  • Fock space representations
  • Graded dimension formulas
  • Quiver Hecke algebras
  • Standard tableaux
  • Young walls

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