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INVARIANT PRIME IDEALS IN QUANTIZATIONS OF NILPOTENT LIE ALGEBRAS
 

Summary: INVARIANT PRIME IDEALS IN QUANTIZATIONS OF
NILPOTENT LIE ALGEBRAS
MILEN YAKIMOV
Abstract. De Concini, Kac and Procesi defined a family of subalgebras Uw
+
of a quantized universal enveloping algebra Uq(g), associated to the elements
of the corresponding Weyl group W. They are deformations of the univer-
sal enveloping algebras U(n+ Adw(n-)) where ną are the nilradicals of a
pair of dual Borel subalgebras. Based on results of Gorelik and Joseph and
an interpretation of Uw
+ as quantized algebras of functions on Schubert cells,
we construct explicitly the H invariant prime ideals of each Uw
+ and show
that the corresponding poset is isomorphic to Ww
, where H is the group
of group-like elements of Uq(g). Moreover, for each H-prime of Uw
+ we con-
struct a generating set in terms of Demazure modules related to fundamental
representations.
Using results of Ramanathan and Kempf we prove similar theorems for

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics