Spectra and catenarity of multiparameter quantum Schubert cells

Abstract

We study the ring theory of the multiparameter deformations of the quantum Schubert cell algebras obtained from 2-cocycle twists. This is a large family, which extends the Artin-Schelter-Tate algebras of twisted quantum matrices. We classify set theoretically the spectra of all such multiparameter quantum Schubert cell algebras, construct each of their prime ideals by contracting from explicit normal localizations, and prove formulas for the dimensions of their Goodearl-Letzter strata for base fields of arbitrary characteristic and all deformation parameters that are not roots of unity. Furthermore, we prove that the spectra of these algebras are normally separated and that all such algebras are catenary.