Le radical quasi-hereditaire des q-algebres de schur
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La th�orie des repr�sentations des alg�bres quasi-h�r�ditaires, qui ont �t� introduites par Cline, Parshall et Scott en 88. Un exemple important est l''alg�bre de Schur, qui a son origine dans la th�orie des repr�sentations polyn�miales de GL_n, ou plus g�n�rale la q-alg�bre de Schur introduite par Dipper et James en 89. On �tudie le radical quasi-h�r�ditaire. d''une telle alg�bre, et d''un point de vue th�orique et autre de vue algorithmique. Ce radical a �t� presente par Geck, avec un append. par Donkin. Le chap. 1 contient une pr�sentation synth�tique des d�fi. et r�sultats principaux sur les alg�bres quasi- h�r�ditaire. Dans le chap. 2, nous d�veloppons des m�thodes explicites pour �tudier en d�tail les repr�sent. de l''alg�bre de Schur S(2, r). En particulier, nous avons des programmes en GAP pour calculer les modules de Weyl et le radical quasi-h�r�ditaire, entre la Conjecture de James et la th�orie des cellules de Kazhdan-Lusztig. C''est le chap. 3. Un r�sultat de ce type se trouve d�j� dans l''article de Geck mentionn� ci- dessus, mais la d�monstration utilise une certaine identit� qui est fausse.
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