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arXiv · 1103.3451

Strata of prime ideals of De Concini-Kac-Procesi algebras and Poisson geometry

Milen Yakimov
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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 Goodearl-Letzter 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].

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Milen Yakimov. 2011-06-19. Strata of prime ideals of De Concini-Kac-Procesi algebras and Poisson geometry. https://arxiv.org/abs/1103.3451

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