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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 10th 2012
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 1st 2015

    added to metaplecitc group the definition of Mp cMp^c (here), a U(1)U(1)-extension of the symplectic group.

    Hm, given a symplectic vector space there is also the restriction of the quantomorphims group to linear symplectomorphisms, which also gives a U(1)U(1)-extension of the symplectic group. Is this Mp cMp^c?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 1st 2015

    That other U(1)U(1)-extension that I mean is called the “extended symplectic group” in section 9 of Robbin-Salamon 93. Their prop. 10.1 goes in the direction of the above question.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 2nd 2015

    I have expanded a litte bit more at metaplectic group; added a bit more on the various definitions, and added more pointers to the literature.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 2nd 2015

    Is this fact from Wikipedia worth developing here?

    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.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 2nd 2015

    Yes, that’s a good point. There are some comments on the on the nnLab at metaplectic correction – Induced inner product, but maybe this deserves to be expanded further.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 2nd 2015

    Added also MU cMU^c (somewhat unforturnate notation…) here and the induced obstruction theory for Mp cMp^c-structure here.

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