fundamental representations
in [Math]
|
Prev: history of sciences and deciding-evidence Chapt 2 #167; ATOM TOTALITY
Next: heavy water in comets is already proof Re: Additive Creation; Dirac's new radioactivities Chapt 5 #169; ATOM TOTALITY
From: metroplex021 on 15 Jun 2010 15:15 Hi folks - I have a couple of basic questions about fundamental representations. First of all, does every group have a set of fundamental representations, or just the semi-simple groups? Secondly, I know that in the case of the (compact?) semi-simple groups, any other representation of the group can be constructed by taking tensor products of its L fundamental representations, where L is the group's rank. Is this the case for all groups, or just the semi-simple ones? Any help would be really appreciated. Thanks!
From: Maarten Bergvelt on 15 Jun 2010 19:38
On 2010-06-15, metroplex021 <fourthinternational(a)googlemail.com> wrote: > Hi folks - I have a couple of basic questions about fundamental > representations. > > First of all, does every group have a set of fundamental > representations, or just the semi-simple groups? What do you mean by fundamental representation of a group. For instance, a finite group has (over the complex numbers, say) n irreducible representations, where n is the number of conjugacy classes. Would you count them as fundamental? Every (finite dim) reps will be a sum of irreducibles. But if you take other groups it might not longer be true that any reps is a sum of irreps, for instnce solvable groups. So what do you take as fundamental reps? > Secondly, I know that in the case of the (compact?) semi-simple > groups, any other > representation of the group can be constructed by taking tensor > products of its L fundamental representations, where L is the group's > rank. Is this the case for all groups, or just the semi-simple ones? -- Maarten Bergvelt |