Primitive ideals in quantum Schubert cells: Dimension of the strata

Bell, J. and Casteels, K. and Launois, S. (2012) Primitive ideals in quantum Schubert cells: Dimension of the strata. Forum Mathematicum . ISSN 0933-7741 (print); 1435-5337 (online). (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1515/forum-2011-0155

Abstract

The aim of this paper is to study the representation theory of quantum Schubert cells. Let be a simple complex Lie algebra. To each element w of the Weyl group W of , De Concini, Kac and Procesi have attached a subalgebra Uq[w] of the quantised enveloping algebra Uq(). Recently, Yakimov showed that these algebras can be interpreted as the (quantum) Schubert cells on quantum flag manifolds. In this paper, we study the primitive ideals of Uq[w]. More precisely, it follows from the Stratification Theorem of Goodearl and Letzter, and from recent works of Mériaux–Cauchon and Yakimov, that the primitive spectrum of Uq[w] admits a stratification indexed by those elements vW with vw in the Bruhat order. Moreover each stratum is homeomorphic to the spectrum of maximal ideals of a torus. The main result of this paper gives an explicit formula for the dimension of the stratum associated to a pair.

Item Type: Article
Additional information: Published online January 2012.
Uncontrolled keywords: Primitive ideals; quantum Schubert cells
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA252 Lie algebras
Q Science > QA Mathematics (inc Computing science) > QA252 Lie algebras
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Stephane Launois
Date Deposited: 04 Oct 2012 08:28
Last Modified: 04 Sep 2013 13:16
Resource URI: http://kar.kent.ac.uk/id/eprint/31241 (The current URI for this page, for reference purposes)
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