TY - JOUR
T1 - Representations of quantized coordinate algebras via PBW-type elements
AU - Oya, Hironori
N1 - Funding Information:
The author is greatly indebted to Yoshiyuki Kimura for his significant comments on the first draft of this paper, and to Yuki Arano for discussions concerning Subsection 6.2. He appreciates the supervision of Yoshihisa Saito. He also would like to thank Ryo Sato and Toshiyuki Tanisaki for many helpful discussions and comments. This work was supported by Grant-in-Aid for JSPS Fellows (No. 15J09231) and the Program for Leading Graduate Schools, MEXT, Japan.
PY - 2018/1
Y1 - 2018/1
N2 - 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.
AB - 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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M3 - Article
AN - SCOPUS:85040732944
VL - 55
SP - 71
EP - 115
JO - Osaka Journal of Mathematics
JF - Osaka Journal of Mathematics
SN - 0030-6126
IS - 1
ER -