2014/12/21 by Yang Zeng, Zeng, Yang, Bin Shu +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.1412.6805
In this paper we formulate a conjecture about the minimal dimensional representations of the finite W-superalgebra U(\mathfrakg_\bbc,e) over the field of complex numbers and demonstrate it with examples including all the cases of type A. Under the assumption of this conjecture, we show that the lower bounds of dimensions in the modular representations of basic Lie superalgebras are attainable. Such lower bounds, as a super-version of Kac-Weisfeiler conjecture, were formulated by Wang-Zhao in \citeWZ for the modular representations of a basic Lie superalgebra \ggg\bbk over an algebraically closed field \bbk of positive characteristic p.