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