Lie Group Representations I: Proceedings of the Special Year by Thomas J. Enright (auth.), Rebecca Herb, Ronald Lipsman,

By Thomas J. Enright (auth.), Rebecca Herb, Ronald Lipsman, Jonathan Rosenberg (eds.)

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Extra resources for Lie Group Representations I: Proceedings of the Special Year held at the University of Maryland, College Park, 1982–1983

Example text

Is true on to a W e y l out that and of its annihilator. 2). module and B r y l i n s k i computation ideals conjectures quo- connection between completely 36 prime p r i m i t i v e tations socle ideals of the e n v e l o p i n g of the c o r r e s p o n d i n g of all such q u o t i e n t are u n i t a r i z a b l e For r e g u l a r from work complex group. algebras, viewed and all u n i t a r y integral of E n r i g h t be a c o n s e q u e n c e algebra central Conjecturally as modules representations characters and P a r t h a s a r a t h y , of a rather and u n i t a r y natural the in this manner.

8). of c a t e g o r i e s so-called techniques in the results. ponding work and f u r t h e r m o r e combinatorial by the p r i m i t i v e Brylinski above by Goldie (Sect. shown that the Duflo rank polynomials. concerning results gave information developing established group d e f i n e d gave also ring for the symmetric (Sect. rem. 4) (roughly is used modules results primitives principal led to the Duflo A more p r e c i s e quotients for the corres- of Kostant, series theorem. formulation the c a t e g o r y in r e f i n i n g it was the c o r r e s p o n d i n g module, For modules an with of h i g h e s t the a d d i t i v i t y an this early established of such H a r i s h - C h a n d r a speaking of the e n v e l o p - the weight principle for 34 Goldie rank based Vogan's on the use of Small's t h e o r e m on i n c l u s i o n The t r a n s l a t i o n principle of the main techniques say the category 0 this allows other with ranks thus giving chamber this w h i c h defined is t e n s o r e d leads essentially r-clans.

The a l g e b r a i c subgroup bA ~ E A+; deduced the whole denote identifies for A. in a c o m p o s i t i o n that so f r o m VM E O b _0A. E @ M : E COb showed fails (where and ~ I m 9. modules. E, a homomor- M to the in (or s i m p l y , occurs M~ Chap. 2) through Let L functor can be rather non runs bA b(w,w') := [M(wl):L(w'l)] times Jantzen U(g) VE E O b matrix L(~) lie that form on to r e s t r i c t dimensional the Jantzen that weights E ® M e Ob O£ We define such advantageous whose finite We note of NG(H)/H G adjoint with Lie and we have G = ~ group of algebra g b and B (resp.

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