English

On small modules for quantum groups at roots of unity

Representation Theory 2016-07-20 v2 Quantum Algebra

Abstract

A conjecture of De Concini Kac and Procesi provides a bound on the minimal possible dimension of an irreducible module for quantized enveloping algebras at an odd root of unity. We pose the problem of the existence of modules whose dimension equals this bound. We show that this question cannot have a positive answer in full generality and discuss variants of this question.

Keywords

Cite

@article{arxiv.1512.04724,
  title  = {On small modules for quantum groups at roots of unity},
  author = {Giovanna Carnovale and Iulian I. Simion},
  journal= {arXiv preprint arXiv:1512.04724},
  year   = {2016}
}

Comments

Minor modifications suggested by the referees. The final publication will appear in Bollettino dell'Unione Matematica Italiana and will be available at Springer via http://dx.doi.org/10.1007/s40574-016-0094-9

R2 v1 2026-06-22T12:10:05.762Z