Strata of prime ideals of De ConciniKacProcesi algebras and Poisson geometry
Abstract
To each simple Lie algebra g and an element w of the corresponding Weyl group De Concini, Kac and Procesi associated a subalgebra U^w_ of the quantized universal enveloping algebra U_q(g), which is a deformation of the universal enveloping algebra U(n_ \cap w(n_+)) and a quantization of the coordinate ring of the Schubert cell corresponding to w. The torus invariant prime ideals of these algebras were classified by Mériaux and Cauchon [25], and the author [30]. These ideals were also explicitly described in [30]. They index the the GoodearlLetzter strata of the stratification of the spectra of U^w_ into tori. In this paper we derive a formula for the dimensions of these strata and the transcendence degree of the field of rational Casimirs on any open Richardson variety with respect to the standard Poisson structure [15].
 Publication:

arXiv eprints
 Pub Date:
 March 2011
 DOI:
 10.48550/arXiv.1103.3451
 arXiv:
 arXiv:1103.3451
 Bibcode:
 2011arXiv1103.3451Y
 Keywords:

 Mathematics  Quantum Algebra;
 Primary 16W35;
 Secondary 20G42;
 14M15
 EPrint:
 15 pages, AMSLatex, v. 2 contains extended Sect. 4