Osaka Journal of Mathematics

Representations of quantized coordinate algebras via PBW-type elements

Hironori Oya

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Inspired by the work of Kuniba-Okado-Yamada, we study some tensor product representations of quantized coordinate algebras of symmetrizable Kac-Moody Lie algebras in terms of quantized enveloping algebras. As a consequence, we describe structures and properties of certain reducible representations of quantized coordinate algebras. This paper includes alternative proofs of Soibelman's tensor product theorem and Kuniba-Okado-Yamada's common structure theorem based on our direct calculation method using global bases.

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Osaka J. Math., Volume 55, Number 1 (2018), 71-115.

First available in Project Euclid: 11 January 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Oya, Hironori. Representations of quantized coordinate algebras via PBW-type elements. Osaka J. Math. 55 (2018), no. 1, 71--115.

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