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 -