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.
Bibliographical noteFunding Information:
The research of M. Kashiwara was supported by Grant-in-Aid for Scientific Research (B) 20H01795, Japan Society for the Promotion of Science.
The research of S.-j. Oh was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2022R1A2C1004045).
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
- Cluster algebra
- Dynkin quiver
- Quantum Cartan matrix
- Quantum affine algebra