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FINITE CONVERGENT PRESENTATIONS OF PLACTIC MONOIDS FOR SEMISIMPLE LIE ALGEBRAS

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Nohra Hage
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Abstract

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.
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ujm-01248274 , version 1 (24-12-2015)

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Nohra Hage. FINITE CONVERGENT PRESENTATIONS OF PLACTIC MONOIDS FOR SEMISIMPLE LIE ALGEBRAS. 2015. ⟨ujm-01248274⟩
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