Hello,
I thought that working with Group Theory for my GSoC 2013 project would be
ideal.
I have familiarized myself with the GAP library and their approach to group
theory
problems, and have a fairly extensive knowledge of group theory (at the
undergraduate
level, at any rate).
The standa
It's not clear from your email if you have looked at what SymPy has already,
or if you have looked at the archives of the sympy list to see what
previous replies
on this topic are. It is also not clear what exactly the procedure for
implementing
character theory would be. (GAP for example uses a lo
I'm referring to the dual group in the context of the Petery-Weyl theorem
from harmonic analysis, which applies to any compact group. The dual group
consists of irreducible homomorphisms from the group to the space of
unitary operators. And by matrix representations, I mean defining the
element
I'm referring to the dual group in the context of the Petery-Weyl theorem
from harmonic analysis, which applies to any compact group. The dual group
consists of irreducible homomorphisms from the group to the space of
unitary operators. And by matrix representations, I mean defining the
element
On Tue, Apr 23, 2013 at 7:27 PM, Tyler Hannan wrote:
> I'm referring to the dual group in the context of the Petery-Weyl theorem
> from harmonic analysis, which applies to any compact group. The dual group
> consists of irreducible homomorphisms from
>
The Peter-Weyl Theorem does not refer to a "
Actually, the Peter-Weyl Theorem is a generalization of the Pontryagin
duality, and by extending the definition of the homomorphisms from the
circle group to generalized unitary matricies asserts the existence of an
algebraic dual group even if the group is not necessarily abelian. I
referenced
On Tue, Apr 23, 2013 at 7:56 PM, Tyler Hannan wrote:
> Actually, the Peter-Weyl Theorem is a generalization of the Pontryagin
> duality, and by extending the definition of the homomorphisms from the
> circle group to generalized unitary matricies asserts the existence of an
> algebraic dual group
Never mind, you're correct. I was thinking of the Tannaka-Krein duality,
which shows the representations form a monoid.
I regards to your reference to GAP's matrix representation system, I was
actually thinking of using the matrix representation for my implementation
to store and compute the pr
