2012/03/16 by Joel Geiger, Geiger, Joel, Milen Yakimov +1
Mathematics · #14M15 #FOS: Mathematics #Primary 16T20 #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Secondary 17B37 #math.QA #math.RA #msc:14M15 #msc:16T20 #msc:17B37
paper · pdf · doi:10.48550/arxiv.1203.3780
29 pages, AMS Latex, minor changes in v. 2
arxiv created 2014/01/03 · arxiv updated 2014/01/06
We resolve two questions of Cauchon and Meriaux on the spectra of the quantum Schubert cell algebras U-[w]. The treatment of the first one unifies two very different approaches to Spec U-[w], a ring theoretic one via deleting derivations and a representation theoretic one via Demazure modules. The outcome is that now one can combine the strengths of both methods. As an application we solve the containment problem for the Cauchon-Meriaux classification of torus invariant prime ideals of U-[w]. Furthermore, we construct explicit models in terms of quantum minors for the Cauchon quantum affine space algebras constructed via the procedure of deleting derivations from all quantum Schubert cell algebras U-[w]. Finally, our methods also give a new, independent proof of the Cauchon-Meriaux classification.