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
Recommended Citation
Tingley, Peter. Elementary Construction of Lusztig’s Canonical Basis. Contemporary Mathematics: Groups, Rings, Group Rings, and Hopf Algebras, 688, : 12, 2017. Retrieved from Loyola eCommons, Mathematics and Statistics: Faculty Publications and Other Works, http://dx.doi.org/10.1090/conm/688
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Copyright Statement
© American Mathematical Society 2017
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