FINITE CONVERGENT PRESENTATIONS OF PLACTIC MONOIDS FOR SEMISIMPLE LIE ALGEBRAS

Nohra Hage (1)

1 AGL - Algèbre, géométrie, logique

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.

Keywords: Plactic algebra; Littelmann path model; standard tableau; convergent presentations

Domains: Representation Theory [math.RT]

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