PROFILPELAJAR.COM

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Untitled

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Its elements can be written explicitly as pairs (A, f) where A =

{ab \choose cd}

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 =

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

is in SL₂(R) and

Michael Hardy 00:41, 24 October 2005 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2005-10-24T00:41:00.000Z","author":"Michael Hardy","type":"comment","level":1,"id":"c-Michael_Hardy-2005-10-24T00:41:00.000Z-Untitled","replies":[]}}-->

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)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2005-10-25T05:22:00.000Z","author":"Fropuff","type":"comment","level":1,"id":"c-Fropuff-2005-10-25T05:22:00.000Z-Untitled","replies":[]}}-->

Yes, I was confusing it with SL_2n(R). R.e.b. 14:11, 25 October 2005 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2005-10-25T14:11:00.000Z","author":"R.e.b.","type":"comment","level":1,"id":"c-R.e.b.-2005-10-25T14:11:00.000Z-Untitled","replies":[]}}-->

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Multiplication in metaplectic group

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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)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2006-11-28T15:07:00.000Z","author":"Daqu","type":"comment","level":2,"id":"c-Daqu-2006-11-28T15:07:00.000Z-Multiplication_in_metaplectic_group","replies":[]}}-->

I'd like to add to this request to clarify the multiplication law. I don't see where j(g*z) is defined. Thanks! —Preceding unsigned comment added by Yzarc314 (talk • contribs) 03:19, 6 July 2010 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2010-07-06T03:19:00.000Z","author":"Yzarc314","type":"comment","level":1,"id":"c-Yzarc314-2010-07-06T03:19:00.000Z-Multiplication_in_metaplectic_group","replies":[]}}-->

Typographical correction

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One should write "modern" instead of "modren" at the end of the article.

Damien

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Assessment comment

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The comment(s) below were originally left at Talk:Metaplectic group/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Field is really tricky to determine (Analysis, Number theory, Algebra are all arguable). The article does not do justice to all the applications of metaplectic group, especially in the section on Weil representation. Perhaps, that section needs to me forked. Arcfrk 10:41, 24 June 2007 (UTC)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2007-06-24T10:41:00.000Z","author":"Arcfrk","type":"comment","level":1,"id":"c-Arcfrk-2007-06-24T10:41:00.000Z-Assessment_comment","replies":[]}}-->

Last edited at 10:41, 24 June 2007 (UTC). Substituted at 02:20, 5 May 2016 (UTC)