We study rewriting properties of the column presentation of plactic monoid for any semisimple Lie algebra such as termination and confluence. Littelmann described this presentation using L-S paths generators. Thanks to the shapes of tableaux, we show that this presentation is finite and convergent. We obtain as a corollary that plactic monoids for any semisimple Lie algebra satisfy homological finiteness properties.
Deformations of symplectic singularities and Orbit method for semisimple Lie algebras
Cyclic wide subalgebras of semisimple Lie algebras
Primitive ideals in the affinoid enveloping algebras of semisimple Lie algebras
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