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Metaplectic Group

The metaplectic group Mp(2n,R) is the connected double cover of the symplectic group Sp(2n,R). Thus it fits into the exact sequence

1->{1,-1}->Mp(2n,R)->Sp(2n,R)->1.

It has a distinguished infinite-dimensional unitary representation, the metaplectic representation, which acts on square-integrable functions and lifts the projective action of the symplectic group arising in Fourier analysis.

See also

Covering Space, Group Representation, Symplectic Group

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References

Folland, G. B. Harmonic Analysis in Phase Space. Princeton, NJ: Princeton University Press, 1989.

Cite this as:

Weisstein, Eric W. "Metaplectic Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MetaplecticGroup.html

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