%0 Unpublished work %T FINITE CONVERGENT PRESENTATIONS OF PLACTIC MONOIDS FOR SEMISIMPLE LIE ALGEBRAS %+ Algèbre, géométrie, logique (AGL) %A Hage, Nohra %8 2015-12-24 %D 2015 %Z 1512.07813 %K Plactic algebra %K Littelmann path model %K standard tableau %K convergent presentations %Z Mathematics [math]/Representation Theory [math.RT]Preprints, Working Papers, ... %X 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. %G English %2 https://ujm.hal.science/ujm-01248274/document %2 https://ujm.hal.science/ujm-01248274/file/LittelmannPaths.pdf %L ujm-01248274 %U https://ujm.hal.science/ujm-01248274 %~ UNIV-ST-ETIENNE %~ CNRS %~ ICJ %~ UNIV-LYON1 %~ INSA-LYON %~ EC-LYON %~ INSMI %~ ICJ-AGL %~ INSA-GROUPE %~ UDL %~ UNIV-LYON %~ ANR