nLab
representation theory of the special unitary group
Contents
Context
Representation theory
representation theory

geometric representation theory

Ingredients
Definitions
representation , 2-representation , ∞-representation

group , ∞-group

group algebra , algebraic group , Lie algebra

vector space , n-vector space

affine space , symplectic vector space

action , ∞-action

module , equivariant object

bimodule , Morita equivalence

induced representation , Frobenius reciprocity

Hilbert space , Banach space , Fourier transform , functional analysis

orbit , coadjoint orbit , Killing form

unitary representation

geometric quantization , coherent state

socle , quiver

module algebra , comodule algebra , Hopf action , measuring

Geometric representation theory
D-module , perverse sheaf ,

Grothendieck group , lambda-ring , symmetric function , formal group

principal bundle , torsor , vector bundle , Atiyah Lie algebroid

geometric function theory , groupoidification

Eilenberg-Moore category , algebra over an operad , actegory , crossed module

reconstruction theorems

Theorems
Contents
Idea
The representation theory of the special unitary group .

Properties
Irreps
The irreps of $SU(n)$ are those polynomial irreps of GL(n,C) , hence those irreps of $SL(n,\mathbb{C})$ , which are labeled by partitions /Young diagrams $\lambda \in Part(n)$ with $rows(\lambda) \leq n - 1$ .

(e.g. Peluse 14, p. 14))

Dimension of irreps and hook/content
References
Shlomo Sternberg , Section 5 of: Group Theory and Physics , Cambridge University Press 1994

Sarah Peluse , Irreducible representations of $SU(n)$ with prime power degree , Séminaire Lotharingien de Combinatoire 71 (2014), Article B71d (pdf )

Last revised on May 17, 2021 at 04:11:51.
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