Finite W-superalgebras for basic classical Lie superalgebras
Abstract
We consider the finite W-superalgebras for a basic classical Lie superalgebra g associated with an even nilpotent element in g both over the field of complex numbers field and and over a filed of positive characteristic. We present the PBW theorem for these finite W-superalgebrfas. Then we formulate a conjecture about the minimal dimensional representations of of complex finite W-superalgebras, and demonstrate it with some examples. Under the assumption that the conjecture holds, we finally show that the lower bound of dimensions predicted in the super version of Kac-Weisfeiler conjecture formulated and proved by Wang-Zhao in [40] for the modular representations of the basic classical Lie superalgebra with any p-characters can be reached.
Cite
@article{arxiv.1404.1150,
title = {Finite W-superalgebras for basic classical Lie superalgebras},
author = {Yang Zeng and Bin Shu},
journal= {arXiv preprint arXiv:1404.1150},
year = {2014}
}
Comments
82 pages. The main result in the older version is improved. For this, we add Sections 9.3 and 9.4. This is still a primary version. arXiv admin note: text overlap with arXiv:0809.0663 by other authors