TY - JOUR

T1 - The (q, t)-Cartan matrix specialized at q= 1 and its applications

AU - Kashiwara, Masaki

AU - Oh, Se jin

N1 - Funding Information:
The research of M. Kashiwara was supported by Grant-in-Aid for Scientific Research (B) 20H01795, Japan Society for the Promotion of Science.
Funding Information:
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).
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023/2

Y1 - 2023/2

N2 - 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.

AB - 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.

KW - Cluster algebra

KW - Dynkin quiver

KW - Q-data

KW - Quantum Cartan matrix

KW - Quantum affine algebra

UR - http://www.scopus.com/inward/record.url?scp=85146799342&partnerID=8YFLogxK

U2 - 10.1007/s00209-022-03195-1

DO - 10.1007/s00209-022-03195-1

M3 - Article

AN - SCOPUS:85146799342

SN - 0025-5874

VL - 303

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 2

M1 - 42

ER -