Representation theory of Lie groups

coefficients in angular momentum eigenstates of quantum systems

web of far-reaching and influential conjectures about connections between number theory and geometry

In physics, an anyon is a type of quasiparticle so far observed only in two-dimensional systems. In three-dimensional systems, only two kinds of elementary particles are seen: fermions and bosons. Anyons have statistical properties intermediate between fermions and bosons. In general, the operation of exchanging two identical particles, although it may cause a global phase shift, cannot affect observables. Anyons are generally classified as abelian or non-abelian. Abelian anyons, detected by two experiments in 2020, play a major role in the fractional quantum Hall effect.

coefficients coupled with angular momentum

representation of a Lie group on its Lie algebra

irreducible representation of the rotation group SO

distinguished element of a Lie algebra's center

theorem

sum of multiples of four 3j symbols

smooth group homomorphism from a Lie group to the general linear group of a vector space

maximal compact connected Abelian Lie subgroup

representation of the symmetry group of spacetime in special relativity

concept in Lie-algebra representation theory

finite-dimensional irreducible representation of a semisimple Lie group whose highest weight is a fundamental weight

description of characters of irreducible representations of compact Lie groups in terms of their highest weights

symbol used in quantum mechanics

an analogue of the formula det(AB) = det(A) det(B), for matrices with noncommuting entrie

classification of irreducible representations of the Poincaré group

first case of a Lie group that is both compact and non-abelian

group controlling representation theory