Talk:Metaplectic group

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Its elements can be written explicitly as pairs (A, f) where A = is in SL₂(R) and

If A was intended to be a matrix and TeX's matrix environment is too cumbersome when inline rather than dislayed, may I suggest this:

{a\quad b\choose c\quad d}.

What you get is this:

Its elements can be written explicitly as pairs (A, f) where A = is in SL₂(R) and

Michael Hardy 00:41, 24 October 2005 (UTC)

---

Isn't the fundamental group of Sp_2n(R) infinite cyclic for all n (not just n = 1)? I thought the maximal compact subgroup of Sp_2n(R) was isomorphic to U(n) ≅ Sp_2n(R) ∩ SO_2n(R). -- Fropuff 05:22, 25 October 2005 (UTC)

Yes, I was confusing it with SL_2n(R). R.e.b. 14:11, 25 October 2005 (UTC)

[edit] Multiplication in metaplectic group

Would someone be kind enough to complete the article's secondary definition of its subject by specifying just how these pairs (A,f) are supposed to be multiplied? (And while you're at it, how about making precise what the allowable functions f are supposed to be? In particular is the function τ → sqrt(cτ+d) intended to be continuous (no doubt), and it is allowed to take values in the lower half-plane (doubt)?)

Also, two nice additions to the secondary definition as { (A,f} ) would be 1) an explanation of why this is equivalent to the double cover of the symplectic group Sp₂(R), and 2) a mention of whether there is a higher-dimensional version of this secondary definition for the higher-dimensional metaplectic groups.

I am very far from knowledgeable on this subject, so I am suggesting that someone other than myself make these improvements.Daqu 15:07, 28 November 2006 (UTC)