for the representation theory of the group of diffeomorphisms of a smooth manifold M is the initial observation that (for M connected) that group acts transitively...

Lorentz group Representation theory of the Galilean group Representation theory of diffeomorphism groups Particle physics and representation theory Symmetry...

specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic...

formulation Representation theory of the Poincaré group Wigner's classification Pauli–Lubanski pseudovector Representation theory of the diffeomorphism group Rotation...

the more general theory of representation theory of semisimple groups, largely due to Élie Cartan and Hermann Weyl, but the Lorentz group has also received...

diffeomorphism; those equivalent to a diffeomorphism leaving a simple closed curve invariant; and those equivalent to pseudo-Anosov diffeomorphisms....

For such groups, a typical goal of representation theory is to classify all finite-dimensional irreducible representations of the given group, up to isomorphism...

even dimension Dr, where n = 2r. Since the group SO(n) is not simply connected, the representation theory of the orthogonal Lie algebras includes both...

include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in...

any field of characteristic 0). The unitary representation theory of the Heisenberg group is fairly simple – later generalized by Mackey theory – and was...

adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie...

Springer 1967 I. M. Isaacs, Character theory of finite groups, AMS Chelsea 1976 D. S. Passman, Permutation groups, Benjamin 1968 Thompson, John G. (1960)...

field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices...

on homotopy groups. The representation theory of SU(3) is well-understood. Descriptions of these representations, from the point of view of its complexified...

representation theory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups and...

of solutions to Gauss's law and spatial diffeomorphism constraints that led Rovelli and Smolin to consider the loop representation in gauge theories and...

construct M24. PSL groups arise as Hurwitz groups (automorphism groups of Hurwitz surfaces – algebraic curves of maximal possibly symmetry group). The Hurwitz...

simple groups List of small groups Modular representation theory Monstrous moonshine P-group Profinite group Representation theory of finite groups Aschbacher...

larger group, and topologically much simpler, namely contractible – see Kuiper's theorem. List of finite simple groups SL2(R) Representation theory of SL2(R)...

gauge theories in terms of extended objects such as Wilson loops and holonomies. The loop representation is a quantum hamiltonian representation of gauge...

important to diverse areas of mathematics such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's...

all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced...

derivation of this fact) is the symmetry algebra of two-dimensional conformal field theory. Diffeomorphism groups of compact manifolds of larger dimension...

invariance and diffeomorphism invariance reflect a redundancy in the description of the system. An alternative theory of gravitation, gauge theory gravity,...

the representation theory of semisimple Lie algebras is one of the crowning achievements of the theory of Lie groups and Lie algebras. The theory was...

In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups M11, M12, M22, M23 and M24 introduced by Mathieu (1861...

all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced...

called a representation of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups of the general...

operator Representation theory of the symmetric group Representation theory of diffeomorphism groups Permutation representation Affine representation Projective...

In the theory of Lie groups, the exponential map is a map from the Lie algebra g {\displaystyle {\mathfrak {g}}} of a Lie group G {\displaystyle G} to...