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Canonical Bases of Borcherds-Cartan Type

Published online by Cambridge University Press:  11 January 2016

Yiqiang Li  and
Zongzhu Lin
Yiqiang Li
Affiliation:
Department of Mathematics, Yale University, 10 Hillhouse Avenue, P.O. Box 208283, New Haven, CT 06520, USA, yiqiang.li@yale.edu
Zongzhu Lin
Affiliation:
Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA, zlin@math.ksu.edu
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Abstract

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We study the canonical basis for the negative part U- of the quantum generalized Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The algebras U- associated to two different matrices satisfying certain conditions may coincide (6.3). We show that the canonical bases coincide provided that the algebras U- coincide (Theorem 6.3.5). We also answer partially a question by Lusztig in [L3] (Theorem 7.1.1).

Keywords

17B3716G2014L30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 194 , 2009 , pp. 169 - 193
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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