Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now

# Questions tagged [representation-theory]

The systematic study of group representations, which describe abstract groups in terms of linear transformations of vector spaces, such that group elements or their generators are represented as matrices, reducing group-theoretic problems to linear-algebraic ones.

143 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
142 views

### Representation Theory of $SL(2,\mathbb R)$

The representation theory regarding the finite-dimensional representations of $SL(2,\mathbb C)$ is well-understood; namely, they all decompose into irreducibles $V_n$, $\dim(V) = n > 0$. ...
329 views

### explicit matrix elements for a representation decomposed into subgroup by branching rules

I'm looking for a way to construct a representation for a simple Lie group such that one particular subgroup is manifest. I learned the branching rules from Cahn, Georgi and Slansky, but I'm still not ...
355 views

### What type of fields are continuous spin representations?

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a ...
133 views

### What does $\Lambda^{-1}_{\frac{1}{2}}\gamma^\mu\Lambda_{\frac{1}{2}}=\Lambda^\mu_{\phantom{\mu}\nu}\gamma^\nu$ mean?

$$\Lambda^{-1}_{\frac{1}{2}}\gamma^\mu\Lambda_{\frac{1}{2}}=\Lambda^\mu_{\phantom{\mu}\nu}\gamma^\nu$$ In P&S, p. 42: Equation (3.29) says that the $\gamma$ ...
167 views

### Infinite-dimensionality of unitary representations of non-compact simple Lie Groups

I have a question about the argument given in On finite-dimensional unitary representations of non-compact Lie groups. I have been looking for a good proof for this claim for a little while now. I ...
317 views

### Understanding the Monster CFT

I try to understand what the Monster CFT and its possible connection to 3 dimensional gravity at ($c=24$) is about (see https://arxiv.org/abs/0706.3359) To my best understanding (and please correct ...
115 views

### Mathematical Rationale for Fermion and Boson Spin Representations

I am beginning with the statement that: All physical states occur as one dimensional representations of $\mathfrak{S}_n$; they are either bosonic or fermionic. Where a fermionic state of n identical ...
266 views

### Why the Universal Covering Space of a (Spacetime) Symmetry Group?

Potential philosophical issues notwithstanding, it is commonly said that the definition of an elementary particle is an irreducible, unitary representation of the Poincaré group (times a gauge group ...
159 views

### Characters of extra representations in the double group of O

Looking at the character table for $\overline{O}$ (double group of $O$) in a book, I noticed that two out of three of the additional irreps (with respect to the five irreps from $O$ itself) are ...
87 views

### Highest weight unitary representations of $psl(2|2)$

I'm having some trouble understanding how to extend representation theory from Lie algebras to super Lie algebras, in particular with $psl(2|2)$. Ultimately I'm interested in 2D quantum sigma models ...
We recall the definition of a Clifford group (over $n$ qubits) is the set of unitary transformations: $$\{U: UPU^\dagger\in\mathcal{P}\}$$ where $\mathcal{P}$ denotes the corresponding Pauli group (...