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...

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...

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...

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...

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...

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...

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...

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....

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

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

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

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

{\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...

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...

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...

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

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

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...

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...

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

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...

\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...

In mathematics, the equivariant algebraic K-theory is an algebraic K-theory associated to the category Coh G ⁡ ( X ) {\displaystyle \operatorname {Coh}...

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

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...

and an equivariant map from E × X {\displaystyle E\times X} to X n . {\displaystyle X^{n}.} Pulling back u n {\displaystyle u^{n}} by this map gives an...

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...

v of the induced vector bundle V over M can be thought of as an H-equivariant map P → V. This is the point of view we shall adopt. Let X be a vector...