Invariant prime ideals in quantizations of nilpotent Lie algebras
Abstract
De Concini, Kac and Procesi defined a family of subalgebras U^w_+ of a quantized universal enveloping algebra U_q(g), associated to the elements of the corresponding Weyl group W. They are deformations of the universal enveloping algebras U(n_+ \cap Ad_w(n_-)) where n_\pm 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^{\leq w}, where H is the group of group-like elements of U_q(g). Moreover, for each H-prime of U^w_+ we construct a generating set in terms of Demazure modules related to fundamental representations.
Keywords
Cite
@article{arxiv.0905.0852,
title = {Invariant prime ideals in quantizations of nilpotent Lie algebras},
author = {Milen Yakimov},
journal= {arXiv preprint arXiv:0905.0852},
year = {2014}
}
Comments
25 pages, AMS-Latex; v.2 minor changes, corrected typos;