Reductive Dual Pair
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 i...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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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