to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group...

representations. An equivariant map is often called an intertwining map of representations. Also, in the case of a group G, it is on occasion called a G-map. Isomorphic...

maps f : X → Y {\displaystyle f:X\to Y} , and while equivariant topology also considers such maps, there is the additional constraint that each map "respects...

space V with an invariant quaternionic structure, i.e., an antilinear equivariant map j : V → V {\displaystyle j\colon V\to V} which satisfies j 2 = − 1...

vector space V with an invariant real structure, i.e., an antilinear equivariant map j : V → V {\displaystyle j\colon V\to V} which satisfies j 2 = + 1...

f ( g x ) = g f ( x ) {\displaystyle f(gx)=gf(x)} ; i.e., f is an equivariant map. We write F G ( X , Y ) = F ( X , Y ) G {\displaystyle F_{G}(X,Y)=F(X...

of the vector bundle, and the projection to Minkowski space is an equivariant map. Therefore, the Poincaré group also acts on the space of sections....

In mathematics, a Cannon–Thurston map is any of a number of continuous group-equivariant maps between the boundaries of two hyperbolic metric spaces extending...

equivariant maps from this G {\displaystyle G} -set to itself are in bijection with G {\displaystyle G} . But it is easy to see that (1) these maps form...

operation whose result is insensitive to the order of its arguments Equivariant map, a function whose composition with another function has the commutative...

default. The composition of equivariant maps is again an equivariant map. There is a category of representations with equivariant maps as its morphisms. They...

morphisms: equivariant maps composition: the composition of equivariant maps identities: the identity function (which is an equivariant map). The category...

{\text{GL}}(W)} ). Then a tensor of type ρ {\displaystyle \rho } is an equivariant map T : F → W {\displaystyle T:F\to W} . Equivariance here means that T...

with equivariant map P → X {\displaystyle P\to X} ; a morphism from P → T {\displaystyle P\to T} to P ′ → T ′ {\displaystyle P'\to T'} is a bundle map (i...

In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a...

smooth, depending on the setting) and the projection map π {\displaystyle \pi } between them is equivariant: π ∘ g = g ∘ π {\displaystyle \pi \circ g=g\circ...

representation Lie algebra representation Maschke's theorem Schur's lemma Equivariant map Frobenius reciprocity Induced representation Restricted representation...

\pi (g)v=v,\,g\in G\}.} If f : V → W {\displaystyle f:V\to W} is an equivariant map between two representations, then its kernel is a subrepresentation...

operator is defined to be a shift-equivariant linear transformation on polynomials in x {\displaystyle x} that maps x {\displaystyle x} to a nonzero constant...

all g in G and all x in X. Morphisms of G-sets are also called equivariant maps or G-maps. The composition of two morphisms is again a morphism. If a morphism...

section s {\displaystyle s} of E {\displaystyle E} let the corresponding equivariant map be ψ ( s ) {\displaystyle \psi (s)} . The covariant derivative on E...

continuous (with respect to the Cantor topology) and equivariant (with respect to the shift map). More generally, it asserts that the morphisms between...

make the momentum map coadjoint equivariant. However, in general the coadjoint action must be modified to make the map equivariant (this is the case for...

differential geometry, the localization formula states: for an equivariantly closed equivariant differential form α {\displaystyle \alpha } on an orbifold...

In differential geometry, an equivariant differential form on a manifold M acted upon by a Lie group G is a polynomial map α : g → Ω ∗ ( M ) {\displaystyle...

G-sets and whose morphisms are (equivalence classes of) spans of G-equivariant maps. It is a categorification of the Burnside ring of G. Let G be a finite...

The G {\displaystyle G} -equivariant map from E G {\displaystyle EG} to a single point ∗ {\displaystyle *} induces a natural map η: X G = F ( ∗ , X ) G...

which is of independent interest: Lemma — Let p:V → W be a surjective equivariant map between representations. If V is semisimple, then p splits; i.e., it...

:P_{\operatorname {Spin} }\rightarrow P_{\operatorname {SO} }(E)} is an equivariant 2-fold covering map such that π ∘ ϕ = π P {\displaystyle \pi \circ \phi =\pi _{P}\quad...

Chern character is used in the Hirzebruch–Riemann–Roch theorem. The equivariant algebraic K-theory is an algebraic K-theory associated to the category...