Reductive Dual Pair

In the mathematical field of representation theory, a reductive dual pair is a pair of subgroups (G, G′) of the isometry group Sp(W) of a symplectic vector space W, such that G is the centralizer of G′ in Sp(W) and vice versa, and these groups act reductively on W. Somewhat more loosely, one speaks of a dual pair whenever two groups are the mutual centralizers in a larger group, which is frequently a general linear group. The concept was introduced by Roger Howe in an influential preprint of the 1970s, which was ultimately published as Howe (1989a).

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