The (q, t)-Cartan matrix specialized at q= 1 and its applications

Masaki Kashiwara, Se jin Oh

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The (q, t)-Cartan matrix specialized at t= 1 , usually called the quantum Cartan matrix, has deep connections with (i) the representation theory of its untwisted quantum affine algebra, and (ii) quantum unipotent coordinate algebra, root system and quantum cluster algebra of skew-symmetric type. In this paper, we study the (q, t)-Cartan matrix specialized at q= 1 , called the t-quantized Cartan matrix, and investigate the relations with (ii) its corresponding unipotent quantum coordinate algebra, root system and quantum cluster algebra of skew-symmetrizable type.

Original languageEnglish
Article number42
JournalMathematische Zeitschrift
Volume303
Issue number2
DOIs
StatePublished - Feb 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

  • Cluster algebra
  • Dynkin quiver
  • Q-data
  • Quantum Cartan matrix
  • Quantum affine algebra

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