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Canonical Bases of Borcherds-Cartan Type
Published online by Cambridge University Press: 11 January 2016
Abstract
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).
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2009
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