Talk:Symplectic group

message: I'm trying to pull together information on matrix groups and was wondering if someone could answer the following questions.
* When is Sp(2n,F) simple?
* What is the center of Sp(2n,F)?
In particular I'm interested in the case when F is finite, however if the results include R,C or all fields it would be useful to include them.  TooMuchMath 17:47, 15 April 2006 (UTC)
thread_title: Simplicity and center

message: Can someone please flag this page as "in need of attention by an expert"?
The last section is rather rough, and in particular, it implies that "O(3) is isomorphic SU(2)", which is wrong.
Thanks. 
98.223.87.110 (talk) 06:17, 10 May 2008 (UTC)
thread_title: Expert attention needed

message: This topic redirects to this page; presumably this corresponds to Sp(n) (the compact group).
This should be make clear.128.32.107.24 (talk) 21:18, 17 February 2009 (UTC)
thread_title:  Unitary symplectic group 

message: Hello.
There is a well known isomorphism between the groups Sp(2) and Spin(3) and also one between Sp(4) and Spin(5).
Now as everybody knows, Spin(3) is the double cover of SO(3), while Spin(5) is the double cover of SO(5), so you could see SO(3) as a kind of projective version of Sp(2) (and likewise SO(5) as a projective version of Spin(4)).
What I'm wondering is:
* Do all the (unitary) symplectic groups have projective versions, and
* if so, do these projective versions inherit some (non-projective) irreducible representations from their covers, in a similar way that SO(3) inherits the 3-dimensional irrep of Spin(2), and SO(5) inherits the 5-dimensional irrep of Sp(4).
85.224.19.225 (talk) 12:49, 4 April 2009 (UTC)
thread_title:  Projective symplectic groups? 

message: I have removed the following strange plug from the article.  It might just be a clumsily-added relevant reference.  I'm not sure, but I would prefer it if someone (besides the original IP who added it) verify the contents of the article against it.  Obviously, this will require a willingness to read the cited paper before restoring the reference to the article:
--Sławomir Biały (talk) 23:44, 10 November 2010 (UTC)
thread_title:  Reference or plug 

message: The section titled Important subgroups reads as follows, in full:
"
The symplectic group Sp(n) is sometimes written as USp(2n) which is convenient for the following equations. The symplectic group comes up in quantum physics as a symmetry on poisson brackets so it is important to understand its subgroups. Some main subgroups are:
: \mathit{USp}(2n) \supset \mathit{USp}(2n-2)
: \mathit{USp}(2n) \supset \mathit{U}(n) 
: \mathit{USp}(4) \supset O(4)
The symplectic groups are also subgroups of various Lie groups:
: \mathit{SU}(n) \supset \mathit{USp}(n)
: F_4 \supset \mathit{USp}(8)
: G_2 \supset \mathit{USp}(2)
There are also the isomorphisms of the Lie algebras usp(4) = so(5) and usp(2) = so(3) = su(2).
"
Three comments:
1)  It is important for us to learn alternative notations, such as what physicists use.  That is different from saying that the article should suddenly switch notations, as it has done in this section: That is a very bad idea.
2)  There is no reason given that the physicists' notation is "convenient for" the inclusion equations displayed.  If there is a good reason for this, it would be helpful to say what it is.
3)  How the symplectic groups (presumably the quaternionic ones, Sp(n) — but this is not clear) "come[s] up in quantum physics as a symmetry on Poisson brackets" should be either explained, or provided with a link to an explanation.Daqu (talk) 22:02, 14 May 2014 (UTC)
thread_title:  Unclear section of article 

message: Because it is a very bad idea to switch notations in the middle of a math article, I have removed the "USP" and "usp" notations for the symplectic Lie groups and Lie algebras (in the Subgroups section), other than just mentioning that such notations exist and can be useful in some circumstances.
If such notations are used in physics, then maybe they are appropriate for a physics article. But this is a math article, and the "USP" and "usp" notations are not modern mathematical notation.  Nor is it "convenient" for any reader to suddenly experience different notation in  the middle of an article.Daqu (talk) 21:08, 25 July 2014 (UTC)
thread_title:  Using alternative notations in a math article is a very bad idea 

message: Why not use a notation that conforms to the size of the matrices in all cases (including the compact case)? I have seen no reference mixing like this. Also,
:"Although the  notation is more common (and hence used here), it can be confusing in that  is often denoted .""
is something I have never seen. YohanN7 (talk) 05:24, 18 December 2014 (UTC)
thread_title:  Notation