1
$\begingroup$

I couldn't find any reference with the representation theory of this specific case. I found some general stuff but never explicit computations or realizations.

The only thing I found on $SU(2, 1)$ is a little bit about its structure theory on Helgason's book (Differential geometry, Lie Groups and Symmetric Spaces).

And so I ask you, do any of you know if there is something like this in the literature (I phrase this question as a reference request because I think it would be near impossible to give an explicit answer in here)? Actually, at this point, anything on this group would be great, but I do need to know whatever is known about its representation theory.

Bonus question: 1) Refenreces on the relation of the rep. theory of $SU(2, 1)$ and $SL(3)$ 2) The relation to the rep. theory of it's Lie algebra. 3) References on actions of $SU(2, 1)$.

$\endgroup$
1

1 Answer 1

Reset to default
3
$\begingroup$

The answer depends on the meaning of "representation" here. In case you mean "unitary representations" by it, a possible reference is The Structure and Unitary Representations of $SU(2,1)$, where also the finite-dimensional representations of the Lie algebra $\mathfrak{sl}_3(\mathbb{C})$ are classified, and all of your bonus question are answered. A special reference here is $[10]$, a complete PhD-thesis on this topic for $SU(2,1)$ and $S(U(1)\times U(1,1))$. There are many other references as well.

$\endgroup$
1
  • 1
    $\begingroup$ You, sir, are an angel. $\endgroup$ Commented Jun 2, 2016 at 14:04

You must log in to answer this question.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.