Representations of quantized coordinate algebras via PBW-type elements

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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.

Original languageEnglish
Pages (from-to)71-115
Number of pages45
JournalOsaka Journal of Mathematics
Volume55
Issue number1
Publication statusPublished - 2018 Jan

ASJC Scopus subject areas

  • Mathematics(all)

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