The $(q,t)$-Cartan matrix specialized at $q=1$

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 kew-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 quantum unipotent coordinate algebra, root system and quantum cluster algebra of skew-symmetrizable type.

55p ages. 2v 46 pages, references updated, typos corrected. 3v 51 pages, small changes

References in corpus (1)

• Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras

Cited by in corpus (2)

• $t$-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras
• Deformed Cartan matrices and generalized preprojective algebras II: General type