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