[Merged by Bors] - feat(RepresentationTheory/Character): the scalar product of characters is the dimension of the space of equivariant maps #25000
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PR summary fba5c9f154Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Co-authored-by: Frédéric Dupuis <[email protected]>
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…s is the dimension of the space of equivariant maps (#25000) If `V` are `W` are finite-dimensional representations of a finite group, then the scalar product of their characters is equal to the dimension of the space of equivariant maps from `V` to `W`. The current version of mathlib has all the necessary ingredients to prove this, but doesn't for some reason; it only has the case where `V` and `W` are irreducible (i.e. Schur orthogonality). This PR proves the general case and deduces Schur orthogonality from it. Co-authored-by: smorel394 <[email protected]>
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If
VareWare finite-dimensional representations of a finite group, then the scalar product of their characters is equal to the dimension of the space of equivariant maps fromVtoW.The current version of mathlib has all the necessary ingredients to prove this, but doesn't for some reason; it only has the case where
VandWare irreducible (i.e. Schur orthogonality). This PR proves the general case and deduces Schur orthogonality from it.