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SPECTRA AND CATENARITY OF MULTI-PARAMETER QUANTUM SCHUBERT CELLS*

Published online by Cambridge University Press:  01 October 2013

MILEN YAKIMOV
MILEN YAKIMOV*
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803USA email: yakimov@math.lsu.edu
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Abstract

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We study the ring theory of the multi-parameter 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 multi-parameter 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.

Keywords

Primary 16W35Secondary 20G4214M15

Footnotes

*

Dedicated to Kenny Brown and Toby Stafford on the occasion of their 60th birthdays

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