Permutation modules for rank 3 symplectic and orthogonal groups
نویسندگان
چکیده
منابع مشابه
Rank 3 Permutation Modules of the Finite Classical Groups
The cross-characteristic permutation modules for the actions of the finite classical groups on singular 1-spaces of their natural modules are studied. The composition factors and submodule lattices are determined.
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A classification is given of rank 3 group actions which are quasiprimitive but not primitive. There are two infinite families and a finite number of individual imprimitive examples. When combined with earlier work of Bannai, Kantor, Liebler, Liebeck and Saxl, this yields a classification of all quasiprimitive rank 3 permutation groups. Our classification is achieved by first classifying imprimi...
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We describe the structure, including composition factors and submodule lattices, of cross-characteristic permutation modules for the natural actions of the orthogonal groups O± m(3) with m ≥ 6 on nonsingular points of their standard modules. These actions together with those studied in [2] are all examples of primitive rank 3 actions of finite classical groups on nonsingular points.
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We consider the action of H = O(p, q) on the matrix space Mp+q,n(R). We study a certain orbit O of H in the null cone N ⊆ Mp+q,n(R) which supports an eigendistribution dνO for H . Using some identities of Capelli type developed in the Appendix, we determine the structure of G̃ = Sp(2n,R)∼-cyclic module generated by dνO under the oscillator representation of G̃ (the metaplectic cover of G = Sp(2n(...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1985
ISSN: 0021-8693
DOI: 10.1016/0021-8693(85)90142-5