Particle physics and representation theory

Physics-mathematics connection Lie groups and Lie algebras Classical groups General linear GL(n) Special linear SL(n) Orthogonal O(n) Special orthogonal SO(n) Unitary U(n) Special unitary SU(n) Symplectic Sp(n) Simple Lie groups Classical An Bn Cn Dn Exceptional G2 F4 E6 E7 E8 Other Lie groups Circle Lorentz Poincaré Conformal group Diffeomorphism Loop Euclidean Lie algebras Lie group–Lie algebra correspondence Exponential map Adjoint representation Killing formIndex Simple Lie algebra Loop algebra Affine Lie algebra Semisimple Lie algebra Dynkin diagrams Cartan subalgebra Root systemWeyl group Real formComplexification Split Lie algebra Compact Lie algebra Representation theory Lie group representation Lie algebra representation Representation theory of semisimple Lie algebras Representations of classical groups Theorem of the highest weight Borel–Weil–Bott theorem Lie groups in physics Particle physics and representation theory Lorentz group representations Poincaré group representations Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel Glossary Table of Lie groupsvte