Re: irreducible represenation of Lie algebra sl_3

In article <P6a%e.16436$R5.1192@xxxxxxxxxxxxxx>, Timothy Murphy
<tim@xxxxxxxxxxxxxxxxxxxxxx> wrote:

> Christopher J. Henrich wrote:
>
> >> Is there for sl_3 something like to Clebsch-Gordon decomposition
> >> formulae for tensor product of two irreducible representation of sl_2?
> >> Let T_(a,b) and T_(c,d) be two irreducible represenation of sl_3, here
> >> a,b,c,d are natural numbers. What is exact decomposition T_(a,b) x
> >> T_(c,d)? Here x is tensor product.
>
> > There have been lots of papers over the years in the Journal of
> > Mathematical Physics which flail away at the problem and, and some have
> > claimed to solve it.
>
> Surely that is a bit pessimistic.
> I think the irreducible representations of sl(n)
> correspond to the Young diagrams with <= n columns,
> and the rule for multiplying these
> can be found eg in Weyl's Classical Groups.
The irreducible representations of sl(n) do correspond to Young
diagrams. Weyl shows this, and finds the characters of the
representations.

As for rules for multiplying representations, I do not recall that Weyl
discusses them at all. Other people have - I think the leading result
is called the "Littlewood - Richardson rules". But these rules are a
way of counting the multiplicity of an irreducible representation in a
tensor product; they do not resolve the product in the very explicit,
detailed way that I think the OP was asking for.

--
Chris Henrich
http://www.mathinteract.com
God just doesn't fit inside a single religion.
.