The purpose of the paper is to derive formulas that describe the structure of the induced supermodule H 0 G (λ) for the general linear supergroup G = GL(m|n) over an algebraically closed field K of characteristic p = 2. Using these formulas we determine primitiveWe conclude with remarks related to the linkage principle in positive characteristic.

We develop a new approach to highest weight categories C with good (and cogood) posets of weights via pseudocompact algebras by introducing ascending (and descending) quasihereditary pseudocompact algebras. For C admitting a Chevalley duality, we define and investigate tilting modules and Ringel duals of the corresponding pseudocompact algebras. Finally, we illustrate all these concepts on an explicit example of the general linear supergroup GL(1|1).

The structure of a Schur superalgebra S ¼ S(1 j 1, r) in odd characteristic p is completely determined. The algebra S is semisimple if and only if p does not divide r. If p divides r, then simple S-modules are one-dimensional and the quiver and relations of S can be immediately seen from its regular representation computed in this paper. Surprisingly, if p divides r, then S is neither quasi-hereditary nor cellular nor stratified, as one would expect by analogy with classical Schur algebras or Schur superalgebras in characteristc zero. (2000): 17A70 (primary), 20C30 (secondary). Mathematics Subject Classifications

The purpose of this paper is to investigate central elements in distribution algebras Dist(G) of general linear supergroups G = GL(m|n).As an application, we compute explicitly the center of Dist(GL(1|1)) and its image under Harish-Chandra homomorphism.

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