# 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.

1,505 questions
Filter by
Sorted by
Tagged with
12 views

### Understanding a rule related to Young tableau

This is my first time learning Young tableau, and I am struggling with a specific rule. I am reading it from this lecture note. The rule I am confused about is the very last point at the end of page 2....
37 views

48 views

56 views

### Effect of spectral flow on representations of a CFT

In this paper titled Spectral flow and conformal blocks in $AdS_3$ the authors states (See paragraph 2 on page 2), For WZNW models based on compact Lie groups, the spectral flow maps primary states ...
82 views

### What extra observable(s) are needed to label the basis states of a representation of the rotation group $N$-dimensional space?

In $3$-dimensional space, any given irreducible representation of the rotation group has a basis whose states are uniquely labeled by the eigenvalues $m$ of a single observable $J_z$, which is one of ...
37 views

### Triplet states, Dicke states and symmetric spin-1 states

When adding two spin-1/2 particles, it is well known that the basis of the composite system can be written in terms of the spin singlet and triplet states. These sates have a well defined symmetry ...
44 views

### Distinction between dual space inner product and inner product against which a representation is unitary

Every vector space $|\vec{v}\rangle$ over the field $\mathbb{R}$ or $\mathbb{C}$ contains a dual space, and so if we make an identification between elements in the dual space and the original vector ...
48 views

### What kind of matrix transformations are allowed in general relativity?

In special relativity, one can transform a 4-vector as follows: $$x'=\Lambda x$$ Of course in this case, $\Lambda$ cannot be an arbitrary $4\times 4$ matrix of $\mathbb{M}(4,\mathbb{C})$. For ...
65 views

### Hadrons as tensors of flavor symmetry even though flavor symmetry is broken?

I will briefly summarize what I know and then ask my questions. If you spot mistakes in my summary, please tell me. The idea of flavor symmetry is that massless QCD is invariant under SU(6) ...
28 views

### Discreteness of the general angular momentum in quantum mechanics [duplicate]

When studying the general angular momentum $\textbf{J}$, which is defined as a vector operator with its components being Hermitian operators satisfying the commutation relations \begin{align*} \textbf{...