Topology of Lie groups | Fourier analysis | Theta functions

Metaplectic group

In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p-adic numbers. The construction covers more generally the case of an arbitrary local or finite field, and even the ring of adeles. The metaplectic group has a particularly significant infinite-dimensional linear representation, the Weil representation. It was used by André Weil to give a representation-theoretic interpretation of theta functions, and is important in the theory of modular forms of half-integral weight and the theta correspondence. (Wikipedia).

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Heisenberg group | Group extension | Pontryagin duality | Upper half-plane | Finite field | Local field | Lattice (group) | Automorphic form | Reductive dual pair | Oscillator representation | Spin group | Modular form | André Weil | Theta correspondence | SL2(R) | Stone–von Neumann theorem | Mathematics | Global field | Metaplectic structure | Real number | Faithful representation | Perfect group | Fundamental group | Special linear group | Projective representation | Symplectic group | Theta function | Adele ring | Unitary representation