2013/02/01 by Axtell, Jonathan
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1302.0042
We introduce categories of homogeneous strict polynomial functors, \Pol^\Id,\k and \Pol^\IId,\k, defined on vector superspaces over a field \k of characteristic not equal 2. These categories are related to polynomial representations of the supergroups GL(m|n) and Q(n), respectively. In particular, we prove an equivalence between \Pol^\Id,\k, \Pol^\IId,\k and the category of finite dimensional supermodules over the Schur superalgebra \Sc(m|n,d), \Qc(n,d) respectively provided m,n ≥ d. We also discuss some aspects of Sergeev duality from the viewpoint of the category \Pol^\IId,\k.