Document Type

Article

Publication Date

2017

Publication Title

Contemporary Mathematics: Groups, Rings, Group Rings, and Hopf Algebras

Volume

688

Pages

12

Abstract

In this largely expository article we present an elementary construction of Lusztig’s canonical basis in type ADE. The method, which is essentially Lusztig’s original approach, is to use the braid group to reduce to rank two calculations. Some of the wonderful properties of the canonical basis are already visible: that it descends to a basis for every highest weight integrable representation, and that it is a crystal basis.

Identifier

978-1-4704-4042-8

Comments

Author Posting. © Copyright American Mathematical Society 2017. This article is posted here by permission of The American Mathematical Society for personal use, not for redistribution. The article was published in Contemporary Mathematics: Groups, Rings, Group Rings, and Hopf Algebras, 2017, https://doi.org/10.1090/conm/688

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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Algebra Commons

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