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Restrictions of irreducible representations of classical algebraic groups to root A(1)-subgroups

机译:Restrictions of irreducible representations of classical algebraic groups to root A(1)-subgroups

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摘要

Restrictions of irreducible representations of classical algebraic groups to root A(1)-subgroups, i.e., subgroups of type A(1) generated by root subgroups associated with two opposite roots, are studied. Composition factors of such restrictions are found in the following cases:, for groups of types A(n) with n > 2 and D-n, for groups of type B-n, n > 2, and long root subgroups, for groups of type C, n > 2, and short root subgroups, and for p-restricted representations of A(2)(K), C-2(K) (recall that B-2(K) congruent to C-2(K)), and of B-n(K), n > 2, and short root subgroups. Here we assume that p > 2 for G = B-n(K) or C-n(K). References: 16

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