Re: symplectic group generators
- From: Jannick Asmus <jannick.news@xxxxxx>
- Date: Sat, 11 Jun 2005 17:44:24 +0200
On 08.06.2005 13:39, r_n_tsai wrote:
> I'm studying the symplectic group (over the reals or over a finite
> field of odd characteristic).
> I saw somewhere that the group is generated by three types of elements
> : J,A,and B
>
> J = |0,-I| A = |a 0 | B = |I 0|
> |I, 0| |0 a'| |b I|
>
> here "J","A",and "B" are 2n x 2n matrices; "a" is an invertivle n x n
> matrix and a' is the transpose
> of its inverse; "b" is a symmetric nxn matrix. You can take all these
> to be over the reals, but the
> finite field case is interesting too. I can certainly see that these
> matrices are symplectic, but
> I can't find a proof that they actually generate the group. A
> constructive proof would be ideal; that
> is given an arbitrary symplectic matrix, an algorithm to express it in
> terms of these three types.
>
> Thanks,
>
> R.N.
>
This topic should be included in any basic publication on Siegel modular
forms. I am not sure whether this is in
http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521350522 I
found after some google research. I think it is worth while trying it.
Upon request I could give you a reference to a *German* book if needed.
Just give me a shout.
Best,
J.
.
- References:
- symplectic group generators
- From: r_n_tsai
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