Schensted type correspondence for type $G_{2}$ and computation of the canonical basis of a finite dimensional $U_{q}(G_{2})$-module

Details Schensted type correspondence for type $G_{2}$ and computation of the canonical basis of a finite dimensional $U_{q}(G_{2})$-module Schensted type correspondence for type $G_{2}$ and computation of the canonical basis of a finite dimensional $U_{q}(G_{2})$-module

2002-11-28

arxiv.org/abs/math/0211443v1

Mathematics

Combinatorics

19 pages

Scientific paper

We use Kang-Misra's combinatorial description of the crystal graphs for
$U_{q}(G_{2})$ to introduce the plactic monoid for type $G_{2}$. Then we
describe the corresponding insertion algorithm which yields a Schensted type
correspondence. Next we give a simple algorithm for computing the canonical
basis of any finite dimensional $U_{q}(G_{2})$-module.

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