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

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

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 1st 2015

That other $U(1)$-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 $n$Lab at metaplectic correction – Induced inner product, but maybe this deserves to be expanded further.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJan 2nd 2015

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