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July, 2017 Modules over quantized coordinate algebras and PBW-bases
Toshiyuki TANISAKI
J. Math. Soc. Japan 69(3): 1105-1156 (July, 2017). DOI: 10.2969/jmsj/06931105


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.


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Toshiyuki TANISAKI. "Modules over quantized coordinate algebras and PBW-bases." J. Math. Soc. Japan 69 (3) 1105 - 1156, July, 2017.


Published: July, 2017
First available in Project Euclid: 12 July 2017

zbMATH: 1378.17031
MathSciNet: MR3685038
Digital Object Identifier: 10.2969/jmsj/06931105

Primary: 20G05
Secondary: 17B37

Keywords: PBW-basis , quantized coordinate algebra

Rights: Copyright © 2017 Mathematical Society of Japan


Vol.69 • No. 3 • July, 2017
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