2008/06/27 by Stephen Donkin, Donkin, Stephen, Rudolf Tange +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Finite Group Theory Research #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.0806.4500
arxiv created 2009/02/11 · arxiv updated 2009/12/01
Let k be an algebraically closed field of characteristic p>0, let m,r be integers with m≥1, r≥0 and m≥ r and let S0(2m,r) be the symplectic Schur algebra over k as introduced by the first author. We introduce the symplectic Schur functor, derive some basic properties of it and relate this to work of Hartmann and Paget. We do the same for the orthogonal Schur algebra. We give a modified Jantzen sum formula and a block result for the symplectic Schur algebra under the assumption that r and the residue of 2m mod p are small relative to p. From this we deduce a block result for the orthogonal Schur algebra under similar assumptions. Finally, we deduce from the previous results a new proof of the geometric description of the blocks of the Brauer algebra in characteristic 0 as obtained by Cox, De Visscher and Martin.