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 language | English |
|---|---|
| Pages (from-to) | 71-115 |
| Number of pages | 45 |
| Journal | Osaka Journal of Mathematics |
| Volume | 55 |
| Issue number | 1 |
| Publication status | Published - 2018 Jan 1 |
| Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Representations of quantized coordinate algebras via PBW-type elements. / Oya, Hironori.
In: Osaka Journal of Mathematics, Vol. 55, No. 1, 01.01.2018, p. 71-115.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Representations of quantized coordinate algebras via PBW-type elements
AU - Oya, Hironori
PY - 2018/1/1
Y1 - 2018/1/1
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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UR - http://www.scopus.com/inward/citedby.url?scp=85040732944&partnerID=8YFLogxK
M3 - Article
VL - 55
SP - 71
EP - 115
JO - Osaka Journal of Mathematics
JF - Osaka Journal of Mathematics
SN - 0030-6126
IS - 1
ER -