Departmental Bulletin Paper REPRESENTATIONS OF QUANTIZED COORDINATE ALGEBRAS VIA PBW-TYPE ELEMENTS

Oya, Hironori

55 ( 1 )  , pp.71 - 115 , 2018-01 , Osaka University and Osaka City University, Departments of Mathematics
ISSN:00306126
NCID:AA00765910
Description
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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