Each symplectic group over the field of two elements has two exceptional doubly transitive actions on sets of quadratic forms on the defining symplectic vector space. This paper studies the associated 2-modular permutation modules. Filtrations of these modules are constructed which have subquotients which are modules for the symplectic group over an algebraically closed field of characteristic ...

This paper investigates the tilting modules of the cyclotomic q–Schur algebras, the Young modules of the Ariki–Koike algebras, and the interconnections between them. The main tools used to understand the tilting modules are contragredient duality, and the Specht filtrations and dual Specht filtrations of certain permutation modules. Surprisingly, Weyl filtrations — which are in general more pow...

Order unit spaces with comparability and spectrality properties as introduced by Foulis are studied. We define continuous functional calculus for order the property Borel spectral spaces. Applying conditions of Alfsen Schultz, we characterize that JB-algebras. also prove a characterization Rickart JB-algebras those which every maximal associative subalgebra is monotone σ-complete, extending an ...

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Investigating the direct integral decomposition of von Neumann algebras of bounded module operators on self-dual Hilbert W*-modules an equivalence principle is obtained which connects the theory of direct disintegration of von Neumann algebras on separable Hilbert spaces and the theory of von Neumann representations on self-dual Hilbert A-modules with countably generated Apre-dual Hilbert A-mod...

3. N. Dunford and B. J. Pettis, Linear operators on summable functions, Trans. Amer. Math. Soc. vol. 47 (1940) pp. 323-392. 4. O. Nikodym, Sur une generalisation des integrates de M. Radon, Fund. Math, vol. 15 (1930) pp. 137-179. 5. R. S. Phillips, Integration in convex linear topological space, Trans. Amer. Math. Soc. vol. 48 (1940) pp. 516-540. 6. C. E. Rickart, Integration in a convex linear...

We give some examples of stably free modules which are not self dual.