All Questions
Tagged with gauge-theory rt.representation-theory
8 questions
29
votes
0
answers
1k
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Linking formulas by Euler, Pólya, Nekrasov-Okounkov
Consider the formal product
$$F(t,x,z):=\prod_{j=0}^{\infty}(1-tx^j)^{z-1}.$$
(a) If $z=2$ then on the one hand we get Euler's
$$F(t,x,2)=\sum_{n\geq0}\frac{(-1)^nx^{\binom{n}2}}{(x;x)_n}t^n,$$
on the ...
- 43.2k
12
votes
3
answers
991
views
Representing SU(3) with 3 ropes in 3 dimensions
The short question is: how exactly is SU(3) realized with ropes?
The long question: There is this idea that deformations of a configuration of three infinitely long, flexible ropes that cross each ...
- 221
8
votes
1
answer
167
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Spin networks as functionals on the moduli space of connections modulo gauge transformations on a graph
I have just read a big part of John Baez's nice article Spin network states in Gauge theory. The definitions are quite clear in that article. However, there is a part which is not explained explicitly ...
- 5,215
6
votes
2
answers
1k
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How many principal bundles are there over a given base?
I'm currently considering principal bundles and classifying spaces in the context of gauge theory and a crucial question came to my mind:
Is there a way to say how many (isomorphism classes of) ...
- 241
6
votes
1
answer
560
views
Is there a specific geometric meaning why fractional charges are allowed in SU(N) gauge theories?
So in the standard model of particle physics, there exist particles with fractional charge. What this means geometrically is as follows: We are given a smooth manifold with a principal $U(1)$ bundle $...
- 922
5
votes
1
answer
305
views
In search of a combinatorial proof on particular set of partitions
Given a partition $\lambda=(\lambda_1\geq\lambda_2\geq\dots)$, denote the conjugate partition by $\lambda'=(\lambda_1'\geq\lambda_2'\geq\dots)$. For example, if $\lambda=(4,2,2)$ then $\lambda'=(3,3,1,...
- 43.2k
5
votes
1
answer
337
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partitions into odd parts vs hooks and symplectic contents
Given a partition $\lambda=(\lambda_1\geq\lambda_2\geq\dots)$, denote the conjugate partition by $\lambda'=(\lambda_1'\geq\lambda_2'\geq\dots)$. For example, if $\lambda=(4,2,2)$ then $\lambda'=(3,3,1,...
- 43.2k
0
votes
0
answers
117
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An interesting identity involving skew-Schur functions
Denote $\rho=(-\frac12,-\frac32,-\frac52,\dots)$. I was reading this interesting paper, where in particular, the authors claim that one can get the expression in (2.9)
\begin{align*}
\prod_{k\geq1}(1+...
- 43.2k