# A expression in Group Theory

1. Dec 3, 2007

### princeton118

What does this expression, SU(2,4), mean?

2. Dec 3, 2007

### CompuChip

It's the notation for a specific group. Also see this Wikipedia page, specifically under the "Generalized ... group" section.

3. Dec 3, 2007

### princeton118

But in the Generalized Linear Group the second term in the parentheses is the Field. But here what does the "4" mean?

4. Dec 3, 2007

### morphism

Probably the finite field with 4 elements.

5. Dec 4, 2007

### princeton118

I see thanks!

6. Dec 4, 2007

### Chris Hillman

Correction! Correct field is C with hermitian IP of signature (2,4)

Uh oh, hope the OP sees this! The special unitary group $SU(p,q)$ is the unitary analog of the special orthogonal group $SO(p,q)$. For example, $SO(2,4)$ comes from the pseudo-euclidean inner product
$$\left(\vec{u}, \, \vec{v} \right) = -u_1 \, v_1 - u_2 \, v_2 + u_3 \, v_3 + u_4 \, v_4 + u_5 \, v_5 + u_6 \, v_6$$
and $SU(2,4)$ comes from the hermitian analog. The field is generally the complex numbers for unitary groups or real numbers for orthogonal groups, but other fields can be considered and then an extra letter is added to indicate this.

How annoying! The only hit Google gives me is " Generalized special unitary group" in this version of this WP article which I happen to know is basically correct, but do as I say not as I do: never cite Wikipedia articles because Wikipedia is unstable and unreliable! :grumpy: