Degenerate 0-Schur algebras and Nil-Temperley-Lieb algebras

Bernt Tore Jensen, Xiuping Su, Guiyu Yang

Research output: Contribution to journalArticle

Abstract

In Jensen and Su (J. Pure Appl. Algebra 219(2), 277–307 2014) constructed 0-Schur algebras, using double flag varieties. The construction leads to a presentation of 0-Schur algebras using quivers with relations and the quiver presentation naturally gives rise to a new class of algebras, which are introduced and studied in this paper. That is, these algebras are defined on the quivers of 0-Schur algebras with relations modified from the defining relations of 0-Schur algebras by a tuple of parameters t. In particular, when all the entries of t are 1, we recover 0-Schur algebras. When all the entries of t are zero, we obtain a class of basic algebras, which we call the degenerate 0-Schur algebras. We prove that the degenerate algebras are both associated graded algebras and quotients of 0-Schur algebras. Moreover, we give a geometric interpretation of the degenerate algebras using double flag varieties, in the same spirit as Jensen and Su (J. Pure Appl. Algebra 219(2), 277–307 2014), and show how the centralizer algebras are related to nil-Hecke and nil-Temperley-Lieb algebras.

Original languageEnglish
Pages (from-to)1177-1196
Number of pages21
JournalAlgebra and Representation Theory
Volume23
Early online date4 Apr 2019
DOIs
Publication statusPublished - 30 Jun 2020

Keywords

  • 0-Schur algebras
  • Double flag varieties
  • Nil-Hecke algebras
  • Nil-Temperley-Lieb algebras
  • Quivers

ASJC Scopus subject areas

  • Mathematics(all)

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