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

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)

Cite this

Quantum Twist Maps and Dual Canonical Bases. / Kimura, Yoshiyuki; Oya, Hironori.

In: Algebras and Representation Theory, Vol. 21, No. 3, 01.06.2018, p. 589-604.

Research output: Contribution to journalArticle

Kimura, Yoshiyuki ; Oya, Hironori. / Quantum Twist Maps and Dual Canonical Bases. In: Algebras and Representation Theory. 2018 ; Vol. 21, No. 3. pp. 589-604.
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