Journal of the Mathematical Society of Japan

Modules over quantized coordinate algebras and PBW-bases

Toshiyuki TANISAKI

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Abstract

Around 1990 Soibelman constructed certain irreducible modules over the quantized coordinate algebra. A. Kuniba, M. Okado, Y. Yamada [8] recently found that the relation among natural bases of Soibelman's irreducible module can be described using the relation among the PBW-type bases of the positive part of the quantized enveloping algebra, and proved this fact using case-by-case analysis in rank two cases. In this paper we will give a realization of Soibelman's module as an induced module, and give a unified proof of the above result of [8]. We also verify Conjecture 1 of [8] about certain operators on Soibelman's module.

Article information

Source
J. Math. Soc. Japan, Volume 69, Number 3 (2017), 1105-1156.

Dates
First available in Project Euclid: 12 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1499846520

Digital Object Identifier
doi:10.2969/jmsj/06931105

Mathematical Reviews number (MathSciNet)
MR3685038

Zentralblatt MATH identifier
1378.17031

Subjects
Primary: 20G05: Representation theory
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]

Keywords
quantized coordinate algebra PBW-basis

Citation

TANISAKI, Toshiyuki. Modules over quantized coordinate algebras and PBW-bases. J. Math. Soc. Japan 69 (2017), no. 3, 1105--1156. doi:10.2969/jmsj/06931105. https://projecteuclid.org/euclid.jmsj/1499846520


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