Representation theory
ScienceWISE definitions
Subcategories
Concepts
- 6-j symbol
- 9-j symbol
- Absolutely irreducible
- Additive identity
- Adjoint endomorphism
- Adjoint representation of a Lie group
- Admissible representation
- Affine action
- Affine Hecke algebra
- Algebra homomorphism
- Algebra representation
- Antifundamental representation
- Arithmetical ring
- Arthur conjectures
- Artin algebra
- Artinian ideal
- Artinian ring
- Artin-Rees lemma
- Artin-Wedderburn theorem
- Artin-Zorn theorem
- Ascending chain condition on principal ideals
- Association scheme
- Auslander algebra
- Auslander-Reiten theory
- Azumaya algebra
- B-admissible representation
- Baer ring
- Bézout domain
- Biquaternion
- Birman-Wenzl algebra
- Blattner's conjecture
- Boolean ring
- Borel subalgebra
- Borel-Weil-Bott theorem
- Borel-Weil theorem
- Bose-Mesner algebra
- Brauer algebra
- Brauer-Cartan-Hua theorem
- Brauer group
- Brauer-Nesbitt theorem
- Brauer's theorem on induced characters
- Brauer's three main theorems
- Burau representation
- Burnside ring
- Capelli's identity
- Cartan matrix
- Casimir invariant
- Category of rings
- Cellular algebra
- Central simple algebra
- Character theory
- Classification of Clifford algebras
- Clebsch-Gordan coefficients
- Clifford algebra
- Clifford module
- Clifford theory
- Coadjoint representation
- Coherent ring
- Commutation theorem
- Commutative ring
- Complementary series representation
- Complex conjugate representation
- Complex representation
- Composition algebra
- Composition ring
- Connected ring
- Continuous Spin
- C-semiring
- Cuspidal representation
- Dade isometry
- Decomposition matrix
- Dedekind-Hasse norm
- Deligne-Lusztig theory
- Depth of noncommutative subrings
- Discrete series representation
- Division algebra
- Division ring
- Dominance order
- Dual representation
- Dynkin index
- Equivariant map
- Euclidean domain
- Exceptional character
- Faithful representation
- Finite ring
- Flat map
- Formal power series
- Free algebra
- Free ideal ring
- Freudenthal magic square
- Frobenius-Schur indicator
- Fundamental representation
- Gabriel's theorem
- Gårding domain
- GCD domain
- Generalized Verma module
- Geometric algebra
- G-module
- Goldie's theorem
- Goldman domain
- Graded algebra
- Grosshans subgroup
- Group action
- Group representation
- Haagerup property
- Haboush's theorem
- Harish-Chandra character
- Harish-Chandra class
- Harish-Chandra module
- Hecke algebra
- Hereditary ring
- Highest weight category
- Hopf algebra
- Hopkins-Levitzki theorem
- Idealizer
- Infinitesimal character
- Integral domain
- Invariant subspace
- Inversive ring geometry
- Irreducible element
- Irreducible ideal
- Irreducible ring
- Isotypic component
- Jacobson density theorem
- Jacobson ring
- Jaffard ring
- Jucys-Murphy element
- Kaplansky's conjecture
- Kazhdan-Lusztig polynomial
- Kazhdan's property
- K-finite
- Kirillov character formula
- Kirillov model
- K-module g
- Kostant partition function
- Köthe conjecture
- Krull ring
- Kummer ring
- Kurosh problem
- Langlands classification
- Langlands group
- Laurent polynomial
- Lawrence-Krammer representation
- Levitzky's theorem
- Lie algebra representation
- Lie-Kolchin theorem
- Littelmann path model
- Littlewood-Richardson rule
- Localization of a ring
- Local ring
- Loewy ring
- Maschke's theorem
- Matrix ring
- Mautner's lemma
- Maximal torus
- Minuscule representation
- Modular representation theory
- Molien series
- Monoid ring
- Monomial representation
- Morita equivalence
- Multiplicity-one theorem
- Nakayama algebra
- N!-conjecture
- Nilpotent
- Noetherian ring
- Noncommutative ring
- Noncommutative unique factorization domain
- Numerical polynomial
- Opposite group
- Opposite ring
- Orbit method
- Ore condition
- Ore extension
- Overring
- P-adic Hodge theory
- Parabolic induction
- Partial group algebra
- Partially-ordered ring
- Perfect field
- Perfect ring
- Plancherel measure
- Poisson ring
- Polynomial identity ring
- Polynomial ring
- Positive definite function on a group
- Prehomogeneous vector space
- Prime element
- Prime ring
- Primitive ring
- Principal ideal domain
- Principal ideal ring
- Principal indecomposable module
- Principal series representation
- Product of rings
- Pseudo-ring
- Quasiregular element
- Quasiregular representation
- Quasisymmetric function
- Quaternionic representation
- Quotient ring
- Racah W-coefficient
- Radical of a ring
- Rational representation
- Real closed ring
- Real representation
- Reduced ring
- Reductive dual pair
- Reductive group
- Regular ideal
- Regular local ring
- Regular representation
- Regular ring
- Representation of a Lie group
- Representation of a Lie superalgebra
- Representation rigid group
- Representation ring
- Representation theory of Hopf algebras
- Representation theory of the Galilean group
- Representation theory of the Lorentz group
- Representation theory of the Poincaré group
- Representative function
- Restricted representation
- Riemann-Hilbert correspondence
- Ringel-Hall algebra
- Ring extension
- Ring homomorphism
- Ring of integers
- Ring theory
- Robinson-Schensted correspondence
- Root datum
- Schreier domain
- Schubert variety
- Schur algebra
- Schur functor
- Schur orthogonality relations
- Schur polynomial
- Schur-Weyl duality
- Segal conjecture
- Semifir
- Semi-local ring
- Semiperfect ring
- Semiprime ring
- Semiring
- Semisimple module
- Serial module
- Simple algebra
- Simple ring
- Skolem-Noether theorem
- Specht module
- Springer correspondence
- Square-free
- Stably finite ring
- Steinberg representation
- Subring
- Subring test
- Symmetric algebra
- Symplectic representation
- System of imprimitivity
- Tensor product of algebras
- The Classical Groups
- Tilting theory
- Topological ring
- Total quotient ring
- Triangular matrix ring
- Triple system
- Trivial representation
- Trivial ring
- Unipotent
- Unique factorization domain
- Unitarian trick
- Unit ring
- Universal enveloping algebra
- Valuation ring
- Verma module
- Vertex of a representation
- Von Neumann regular ring
- Wedderburn's little theorem
- Weyl algebra
- Weyl character formula
- Whittaker model
- Wigner 3-j symbols
- Wigner-Eckart theorem
- Witt vector
- Young's lattice
- Young symmetrizer
- Young tableau
- Zero divisor
- Zero-product property
- Zero ring
- Zoghman Mebkhout
- Zorn ring
- Zuckerman functor
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