By Robert J. Blattner (auth.), Prof. Jacques Carmona, Prof. Jaques Dixmier, Prof. Michèle Vergne (eds.)
Read Online or Download Non-Commutative Harmonic Analysis: Actes du Colloque d’Analyse Harmonique Non Commutative, Marseille-Luminy, 1 au 5 Juillet 1974 PDF
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Extra info for Non-Commutative Harmonic Analysis: Actes du Colloque d’Analyse Harmonique Non Commutative, Marseille-Luminy, 1 au 5 Juillet 1974
Sample text
Lemme. 7. Les id~eux premiers de F' sont : 0 B p ~ A : F ' p = pF' et~pour tout t ~ [Bp + B[q-~J )~A = F'p + F'[q-~) = pF' + [ q - X ] F ' Ces id~aux sont compl~tement premiers. Comme A est simple centreie, les id~aux bilat~re~de F' sont les ensembles J | Jest un ideal bilet@re de B. premier) el et seuiement sl J e s t D'autme part J | est premier (resp. compi~tement premier (resp. eompl~tement premier). II s u ~ I t ~ o r s d'utillser la llste connue let ~aclle) des Id~aux premiers de B. 6. Etude de ~ 2 .
Ie p ~ due ~ Mo DUFLO~ des id4aux primitifs radiciels correspondent de Verma de plus haut poids o~ k H- XCH) , pour U(~) dans et IA U(~) op~re scalairement est donm~ par la formule ~ ~ , on associe le module ~ d@fini par est l'id@al ~ gauche de MA , comme annulateurs des modules de Verma, que nous allons r&p-- somme des sous-espaces n~gatives). ~ct(~) ~. peler. Fixons une sous-alg~bre de C~rtam h ~ . ,q n U(~) de car&ct~risti- l'alg~bre enveloppante de Nous n'exposerons icl que les principaux r@s~ita%s.
Peler. Fixons une sous-alg~bre de C~rtam h ~ . ,q n U(~) de car&ct~risti- l'alg~bre enveloppante de Nous n'exposerons icl que les principaux r@s~ita%s. minimaux de k varie darts l'ensemble des id~aux primitifs minimaux - r~ga) les g@n4rateurs U(~) sur un corps U(~) H S ~ . O~ ~ote engendr4 par ~ n et lee 41dments de la la r s ~ e ~ t ~ t i o = =~tur~:le ae son noyau. O= volt facilement que le oentre sur Mk et que lu caract~re ~ A de Z Z de aimsl d~fini 32 ~(~,)-P ( = ) ( X ) o~ P est la projection de u(~) - u(_h) 9 (on identifie En notant U(h) ~ l'al~bre ~+~ et U(~) assooige K la d~oomposi~ion S(h) des fonctious polynOmes a=r ~+~ son intersection I de On note ~~ f Ker~)~ S(~) ~" , M)~ .