Invariant Theory

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4 domain-specific abstractions whose origin domain is Invariant Theory.

• Bracket algebra — A quotient algebra encoding projective invariants through bracket symbols over a signed alphabet.
• Hermite reciprocity — A representation-theoretic isomorphism exchanging degree and symmetric-power indices for binary forms: Sym^m(Symn V) is isomorphic to Sym^n(Symm V) for two-dimensional V.
• Osculant — An invariant that vanishes when hypersurfaces have contact of unusually high order at a common point.
• Pseudoreflection — A finite-order nonidentity linear automorphism whose fixed subspace is a hyperplane.