2014/02/24 by Jonathan Axtell, Axtell, Jonathan
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1402.5808
33 pages; v2 minor corrections
arxiv created 2014/03/26 · arxiv updated 2014/03/27
We introduce super-analogues of the Schur functors defined by Akin, Buchsbaum and Weyman. These \em Schur superfunctors may be viewed as characteristic-free analogues of the finite dimensional atypical irreducible modules over the Lie superalgebra \mathfrakgl(m|n) studied by Berele and Regev. Our construction realizes Schur superfunctors as objects of a certain category of strict polynomial superfunctors. We show that Schur superfunctors are indecomposable objects of this category. Another aim is to provide a decomposition of \em Schur bisuperfunctors in terms of tensor products of Schur superfunctors.