Canonical Bases of Borcherds-Cartan Type

Mathematics – Representation Theory

Scientific paper

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To appear in Nagoya Math J

Scientific paper

We study the canonical basis for the negative part of the quantum generalized
Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The
algebras associated to two different matrices satisfying certain conditions may
coincide. We show that the canonical bases coincide provided that the algebras
coincide. We also answer partially a question by Lusztig.

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