Osaka Journal of Mathematics

Representations of quantized coordinate algebras via PBW-type elements

Hironori Oya

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 11 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1515661217

Mathematical Reviews number (MathSciNet)
MR3744976

Zentralblatt MATH identifier
06848744

Subjects
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]

Citation

Oya, Hironori. Representations of quantized coordinate algebras via PBW-type elements. Osaka J. Math. 55 (2018), no. 1, 71--115. https://projecteuclid.org/euclid.ojm/1515661217


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