Reductive dual pair

In the mathematical field of representation theory, a Howe pair or dual pair is a pair of subgroups (G,H) of the general linear group GL(V) of a vector space V, such that G is the centralizer of H in GL(V) and vice versa. The concept was introduced by Roger Howe in an influential preprint of the 1970s, which was ultimately published in 1989.

References

• Howe, Roger (1989). "Remarks on classical invariant theory", Transactions of the American Mathematical Society 313, pp. 539–570.
• Wallach, Nolan R. and Goodman, Roe (1998). "Representations and Invariants of the Classical Groups" (1998) Cambridge University Press, ISBN 0521663482.