[[Group representation theory MOC]]
# Representation theory of symmetric groups

The representation theory of [[Symmetric group|symmetric groups]] $S_{n}$ is fundamental to group representation theory as a whole by virtue of [[Cayley's theorem]].

## Representations

- [[1-dimensional irreps of a finite symmetric group]]
- [[Characters of a finite symmetric group are real]]
- [[Associate representation]]
- [[Trivial and alternating characters of a finite symmetric group in tensor product decomposition]]


## Group ring

- [[Symmetrizer and antisymmetrizer elements]]
- [[Young operator]]

## Young operators

- [[Numeric partition]], [[Young diagram]], [[Young tableau]]
- [[Young operator]]

#
---
#MOC | #state/develop | #lang/en | #SemBr