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A duality correspondence is set up between polynomials satisfying a recurrence relation and the generalized eigenvectors of a Jacobi operator in a rigged Hilbert space.
We adopt the Langlands classification to the context of real reductive dual pairs and prove that Howe's Duality Correspondence maps hermitian representations to hermitian representations.
We give a complete and explicit description of duality correspondence for p+q⩽n as well as some of the cases for p+q>n, in terms of the Langlands parameters.
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The correspondence principle and the duality rule are used.
We study in detail the relation between the newly introduced dual pairs, the quantum notion of Howe pair, and the symplectic leaf correspondence of Poisson manifolds in duality.
Duality, complexity.
Duality abounds.
Koszul duality and Verdier duality.
Consciousness creates duality.
(See wave-particle duality).
(Enough of this duality).
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