Schensted type correspondence for type G₂ and computation of the canonical basis of a finite dimensional U_q(G₂)-module

2002/11/28 by cedric Lecouvey, Lecouvey, cedric
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA

paper · pdf · doi:10.48550/arxiv.math/0211443

19 pages

arxiv created 2002/11/28 · arxiv updated 2009/11/30

Abstract

We use Kang-Misra's combinatorial description of the crystal graphs for U_q(G₂) to introduce the plactic monoid for type G₂. 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(G₂)-module.

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