2010/09/07 by Jason Bell, Bell, Jason, Karel Casteels +3
Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.AG #math.CO #math.QA #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1009.1347
20 pages
arxiv created 2010/09/07 · arxiv updated 2011/11/09
The aim of this paper is to study the representation theory of quantum Schubert cells. Let \g be a simple complex Lie algebra. To each element w of the Weyl group W of \g, De Concini, Kac and Procesi have attached a subalgebra Uq[w] of the quantised enveloping algebra Uq(\g). 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 that the primitive spectrum of Uq[w] admits a stratification indexed by those primes that are invariant under a natural torus action. 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 given torus-invariant prime.