Summary: INVARIANT PRIME IDEALS IN QUANTIZATIONS OF
NILPOTENT LIE ALGEBRAS
MILEN YAKIMOV
Abstract. De Concini, Kac and Procesi defined a family of subalgebras U w
+
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 n± are the nilradicals of a
pair of dual Borel subalgebras. Based on results of Gorelik and Joseph and
an interpretation of U w
+ as quantized algebras of functions on Schubert cells,
we construct explicitly the H invariant prime ideals of each U w
+ and show
that the corresponding poset is isomorphic to W #w , where H is the group
of group­like elements of Uq (g). Moreover, for each H­prime of U w
+ 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
vanishing ideals of closures of torus orbits of symplectic leaves of related Pois­

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

Collections: Mathematics