Brief Questions re O(N) groups and re the exp[i p x] function

[Jay R. Yablon]

Hello to all:

I have two questions:

1) The group SU(2) contains 3=2^2-1 generators and describes rotations
through O(3) in a 3-dimensional space. The groups SU(N) contains N^2-1
generators. Would it be correct to say that it can be used to describe
rotations through O(N^2-1) in an N^2-1 dimensional space?

2) Just a lexicography question: is the factor exp[i p x] itself called
the mode function? If not, what are the various terms used to refer to
this function?

Thanks,

Jay.
____________________________
Jay R. Yablon
Email: jyablon@nycap.rr.com
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm

[Hans Aberg]

Jay R. Yablon wrote:
> 1) The group SU(2) contains 3=2^2-1 generators and describes rotations
> through O(3) in a 3-dimensional space. The groups SU(N) contains N^2-1
> generators. Would it be correct to say that it can be used to describe
> rotations through O(N^2-1) in an N^2-1 dimensional space?

It looks as though you are asking for the construction of the Pin groups
(Spin without "S", pun on O being SO without "SO").
http://en.wikipedia.org/wiki/Pin_group
They have a Spin subgroup of index two
http://en.wikipedia.org/wiki/Spin_group
which in turn be computed using Clifford algebras
http://en.wikipedia.org/wiki/Clifford_algebra

The table on the Spin group link above shows that Spin(6) = SU(4), a
cover group of SO(6), in turn an index two subgroup of O(6). Here your N
= 4, but N^2-1 = 15, not 6.

Hans