TY - JOUR
T1 - The (q, t)-Cartan matrix specialized at q= 1 and its applications
AU - Kashiwara, Masaki
AU - Oh, Se jin
N1 - 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 affine algebra
KW - Quantum Cartan matrix
UR - https://www.scopus.com/pages/publications/85146799342
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 -