Quantum Twist Maps and Dual Canonical Bases

Yoshiyuki Kimura, Hironori Oya

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincaré-Birkhoff-Witt type bases under the “reverse” lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors.

Original languageEnglish
Pages (from-to)589-604
Number of pages16
JournalAlgebras and Representation Theory
Volume21
Issue number3
DOIs
Publication statusPublished - 2018 Jun 1
Externally publishedYes

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Keywords

  • Dual canonical bases
  • Poincaré-Birkhoff-Witt type bases
  • Quantized universal enveloping algebras
  • Quantum T-systems
  • Quantum twist maps
  • Unipotent quantum minors

ASJC Scopus subject areas

  • Mathematics(all)

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