an:03853246
Zbl 0537.14010
Brylinski, J. L.
Differential operators on the flag varieties
EN
Ast??risque 87-88, 43-60 (1981).
1981
a
14F10 14M15 14L35 14L30 20G15
algebra of global differential operators on the flag variety; Verma module
[For the entire collection see Zbl 0468.00006.]
Let G be a connected semi-simple algebraic group over a field of characteristic 0 and let X be the flag variety of G. The author determines the algebra structure of \(\Gamma\) (X,\({\mathcal D}_ X)\), the algebra of global differential operators on X: Let \(U({\mathfrak G})\) be the enveloping algebra of the Lie-algebra of G, Z be the center of \(U({\mathfrak G})\) and I the ideal \(U({\mathfrak G})\cdot Z(\cap(U({\mathfrak G})\cdot {\mathfrak G}))\). Then \(\Gamma\) (x,\({\mathcal D}_ X)\) is isomorphic to \(U({\mathfrak G})/I\).
F.Pauer
Zbl 0468.00006