Category:Representation theory

• Theorems in representation theory (19 P)

A

• Algebras (11 C, 70 P)

C

• Clifford algebras (3 C, 21 P)

H

• Harmonic analysis (6 C, 64 P)

I

• Invariant subspaces (10 P)
• Invariant theory (1 C, 60 P)

L

• Langlands program (20 P)

M

• Module theory (83 P)

R

• Representation theory of groups (4 C, 41 P)
• Representation theory of Lie algebras (23 P)

• Glossary of representation theory
• List of representation theory topics
• Representation theory

A

• Absolute irreducibility
• Admissible representation
• Affine braid group
• Affine Hecke algebra
• Affine Lie algebra
• Affine symmetric group
• Algebra representation
• Algebraic representation
• Alvis–Curtis duality
• Arthur's conjectures
• Artin conductor
• Association scheme
• Auslander algebra
• Auslander–Reiten theory
• Automorphic Forms on GL(2)

B

• Beilinson–Bernstein localization
• Bernstein–Zelevinsky classification
• Birman–Wenzl algebra
• Borel subalgebra
• Borel–de Siebenthal theory
• Bose–Mesner algebra
• Bott cannibalistic class
• Brauer algebra
• Burau representation

C

• Canonical basis
• Cartan matrix
• Category of representations
• Cellular algebra
• Chang number
• Character (mathematics)
• Character table
• Chevalley restriction theorem
• Chiral algebra
• The Classical Groups
• Clifford module
• Clifford theory
• Coherent set of characters
• Complexification (Lie group)
• Crystal base

D

• Dade isometry
• Dade's conjecture
• Deligne–Lusztig theory
• Demazure conjecture
• Demazure module
• Differential poset
• Dominance order
• Double affine braid group
• Double affine Hecke algebra

E

• Eisenstein integral
• Equivariant map
• Exceptional character

F

• Faithful representation
• Freudenthal magic square
• Frobenius formula
• Frobenius characteristic map
• Fundamental representation

G

• Garnir relations
• Gelfand–Graev representation
• Geometric Langlands correspondence
• Good filtration
• Group representation

H

• Haagerup property
• Harish-Chandra's Schwartz space
• Harish-Chandra's Ξ function
• Hecke algebra (disambiguation)
• Hecke algebra of a pair
• Herz–Schur multiplier
• Highest-weight category
• Hopf algebra
• Hurwitz's theorem (composition algebras)

I

• Invariant convex cone
• Invariant subspace
• Irreducible representation
• Itô's theorem
• Iwahori subgroup
• Iwahori–Hecke algebra

J

• Jacquet module
• Jantzen filtration
• Jucys–Murphy element

K

• Kirillov model
• Kostant partition function
• Kronecker coefficient
• Krull–Schmidt category

L

• Langlands–Deligne local constant
• Langlands–Shahidi method
• Lawrence–Krammer representation
• Littelmann path model
• Littlewood–Richardson rule
• Locally compact quantum group

M

• Maass–Selberg relations
• McKay graph
• Zoghman Mebkhout
• Minimal K-type
• Minuscule representation

N

• N = 2 superconformal algebra
• N! conjecture
• Naimark equivalence
• Nil-Coxeter algebra
• Nonlinear realization

O

• Opposite group
• Oscillator representation

P

• Parabolic induction
• Partition algebra
• Persistence barcode
• Persistence module
• Plancherel measure
• Prehomogeneous vector space
• Principal subalgebra
• Projective representation

Q

• Quantized enveloping algebra
• Quantum affine algebra
• Quaternionic discrete series representation
• Quaternionic representation
• Quiver (mathematics)

R

• Real representation
• Reductive dual pair
• Representation on coordinate rings
• Representation theory of finite groups
• Representation theory of Hopf algebras
• Restricted representation
• Riemann–Hilbert correspondence
• Ringel–Hall algebra
• Root datum

S

• Satake isomorphism
• Schubert polynomial
• Schubert variety
• Schur algebra
• Schur functor
• Schur–Weyl duality
• Schur's lemma
• Semi-invariant of a quiver
• Semi-simplicity
• Semisimple representation
• Shapiro's lemma
• Simple module
• Stable module category
• Steinberg formula
• Subrepresentation
• Symplectic representation

T

• Theorem of the highest weight
• Theta correspondence
• Θ10
• Tilting theory
• Translation functor
• Triple system
• Trivial representation

U

• Uniformly bounded representation
• Unipotent representation

V

• Verlinde algebra
• Vertex of a representation

W

• W-algebra
• Waldspurger formula
• Weil–Brezin Map
• Weyl module
• Whittaker model
• Wild problem

Y

• Yangian
• Young subgroup
• Young's lattice

Z

• Zuckerman functor