Algebraic Groups by Arjeh M. Cohen, Wim H. Hesselink, Wilberd L.J. van der

By Arjeh M. Cohen, Wim H. Hesselink, Wilberd L.J. van der Kallen, Jan R. Strooker

From 1-4 April 1986 a Symposium on Algebraic teams was once held on the college of Utrecht, The Netherlands, in party of the 350th birthday of the college and the sixtieth of T.A. Springer. famous leaders within the box of algebraic teams and similar components gave lectures which lined extensive and relevant components of arithmetic. even though the fourteen papers during this quantity are in general unique study contributions, a few survey articles are incorporated. Centering at the Symposium topic, such different subject matters are lined as Discrete Subgroups of Lie teams, Invariant idea, D-modules, Lie Algebras, exact services, workforce activities on types.

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4. CHARACTERISTIC CLASSOF A PRIMITIVE IDEAL 4~ Characteristic v a r i e t y of a p r i m i t i v e ideal. J ~ Xo, we f i r s t construct a cone-subbundle in f i n e the c h a r a c t e r i s t i c class of J Starting from a p r i m i t i v e ideal T*X as f o l l o w s . 3). Consider the quotient U(g)/J as a l e f t g-module M, and take the correspon- ding sheaf of modules M:= DX~U(g) M over the sheaf Dx l o c a l i z a t i o n of of rings of d i f f e r e n t i a l operators on M on X (Beilinson-Bernstein X); then the c h a r a c t e r i s t i c v a r i e t y resp.

Moreover, there is a geometrical i n t e r p r e t a t i o n f o r these ~ntegers, f o r which i ref e r to our resp. Hotta's o r i g i n a l papers. For example, t h i s says t h a t unless Kj ~6 intersects Ki nij(s) = 0 in codimension ~ I. gebraic c o n s t r u c t i o n of our c h a r a c t e r i s t i c classes. 1. This d e f i n i t i o n - B o r e l ' s d e s c r i p t i o n of t, by a W-equivariant H*(X) - The Chern character bundle on X in terms of polynomials on the Cartan subalgebra isomorphism W-harmonic polynomials on B: H*(X) ~ • S(t_*) ~ onto the space of a l l t.

Left) A-modules. There is a natural isomorphism L N. ~ ~HOmA((M). * , N ' ) . M" ® A These considerations also hold for A a n o e t h e r i a n sheaf of rings (in t h e sense of [21 ]), of finite global homological dimension. One t h e n considers derived categories of bounded complexes of coherent (sheaves of) A-modules. Now in t h e case of the sheaf ~Dx, t h e r e is an equivalence of 52 categories between left 4~x-modules and right 4Jx-modules (see [20, $1] n, for details). Here cox = 9X is t h e canonical sheaf, w h e r e n = d i m (X) .

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