Journal of the Mathematical Society of Japan

Modules over quantized coordinate algebras and PBW-bases

Toshiyuki TANISAKI

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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

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

First available in Project Euclid: 12 July 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

quantized coordinate algebra PBW-basis


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.

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