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).
Read more about Reductive Dual Pair: Examples, Structure Theory and Classification, See Also
Famous quotes containing the words reductive, dual and/or pair:
“In the haunted house no quarter is given: in that respect
It’s very much business as usual. The reductive principle
Is no longer there, or isn’t enforced as much as before.”
—John Ashbery (b. 1927)
“Thee for my recitative,
Thee in the driving storm even as now, the snow, the winter-day
declining,
Thee in thy panoply, thy measur’d dual throbbing and thy beat
convulsive,
Thy black cylindric body, golden brass and silvery steel,”
—Walt Whitman (1819–1892)
“To get a man soundly saved it is not enough to put on him a pair of new breeches, to give him regular work, or even to give him a University education. These things are all outside a man, and if the inside remains unchanged you have wasted your labour. You must in some way or other graft upon the man’s nature a new nature, which has in it the element of the Divine.”
—William Booth (1829–1912)