Proceedings of the Japan Academy, Series A, Mathematical Sciences

Notes on parameters of quiver Hecke algebras

Masaki Kashiwara

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Abstract

Varagnolo-Vasserot and Rouquier proved that, in a symmetric generalized Cartan matrix case, the simple modules over the quiver Hecke algebra with a special parameter correspond to the upper global basis. In this note we show that the simple modules over the quiver Hecke algebras with a generic parameter also correspond to the upper global basis in a symmetric generalized Cartan matrix case.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 88, Number 7 (2012), 97-102.

Dates
First available in Project Euclid: 6 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.pja/1341579087

Digital Object Identifier
doi:10.3792/pjaa.88.97

Mathematical Reviews number (MathSciNet)
MR2946856

Zentralblatt MATH identifier
1257.20005

Subjects
Primary: 05E10: Combinatorial aspects of representation theory [See also 20C30] 16G99: None of the above, but in this section 81R10: Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70]

Keywords
Global basis Khovanov-Lauda-Rouquier algebras categorification

Citation

Kashiwara, Masaki. Notes on parameters of quiver Hecke algebras. Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 7, 97--102. doi:10.3792/pjaa.88.97. https://projecteuclid.org/euclid.pja/1341579087


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