[GAP Forum] SU(n) group

[Asst. Prof. Dmitrii (Dima) Pasechnik]

Dear Krishna,

it depends upon the way your group is given, a lot,
as well as on particular properties of it.

E.g. if it is a finite group you can, by computing the
character table (actually, a part of it)
easily see whether it has a faithful 3-dimensional
complex representation (which will be a unitary
representation), and then, with a bit more effort,
to see whether such a representation is into
SU(3), or not.

For infinite groups this is in general much harder, IMHO.
On the other hand if it is already a subgroup of GL(3) then
this should be easy...

Best,
Dmitrii

On 1 May 2010 19:36, krishna mohan <trebauchet1986 at yahoo.co.in> wrote:
> Hi..
>
>       Suppose I have a group and want to find whether its a subgroup of SU(3). How can I
> do that in GAP?
>
>  Krishna Mohan
> Project Assistant
> CHEP
> Indian Institute of Science
> Bangalore
>>
>
> --- On Fri, 30/4/10, Scott Murray <scott.murray at canberra.edu.au> wrote:
>
> From: Scott Murray <scott.murray at canberra.edu.au>
> Subject: Re: [GAP Forum] SU(n) group
> To: "krishna mohan" <trebauchet1986 at yahoo.co.in>
> Date: Friday, 30 April, 2010, 4:14 PM
>
> Dear Krishna,
>
> It is possible in GAP to define the root datum of SU(n).  I don't
> think you can define the group over the complex numbers.  GAP is not
> designed for numerical analysis.  However, it is useful for
> representation theory problems that reduce to combinatorics of roots
> and weights, like branching and plethysm problems.
>
> If you let me know what specific computation you want to do, I might
> be able to help further.
>
> All the best,
> Scott Murray.
>
>
>
> On 30 April 2010 17:41, krishna mohan <trebauchet1986 at yahoo.co.in> wrote:
>> In GAP, can I define an SU(n) group over complex numbers?
>>
>>
>> Krishna Mohan
>> Project Assistant
>> CHEP
>> Indian Institute of Science
>> Bangalore
>>
>>
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>>
>
>
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--
Dmitrii Pasechnik
-----
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