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

Masaki Kashiwara; Se jin Oh

doi:10.1007/s00209-022-03195-1

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

Masaki Kashiwara, Se jin Oh

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 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.

Original language	English
Article number	42
Journal	Mathematische Zeitschrift
Volume	303
Issue number	2
DOIs	https://doi.org/10.1007/s00209-022-03195-1
State	Published - Feb 2023

Bibliographical note

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.

Keywords

Cluster algebra
Dynkin quiver
Q-data
Quantum Cartan matrix
Quantum affine algebra

Access to Document

10.1007/s00209-022-03195-1

Cite this

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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 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.",

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