Invariants
An invariant is a property or quantity that remains unchanged under a certain group (or monoid, or category) of transformations. Classical invariant theory is concerned with polynomials invariant under group actions, but the concept of an invariant is broader, belonging to the general study of symmetry.
Online resources:
- Per Alexandersson’s catalog of symmetric functions and related polynomials
Literature
Peter Olver ’s first three books are all, directly or indirectly, about invariants:
- Olver, 1993: Applications of Lie Groups to Differential Equations, 2nd ed. (slides)
- Olver, 1995: Equivalence, Invariants, and Symmetry (doi)
- Olver, 1999: Classical Invariant Theory (doi)
Olver also has interesting papers on invariants with applications to object recognition:
- Olver, 2016: The symmetry groupoid and weighted signature of a geometric object (pdf, slides)
- Olver, 2012: Invariant histograms (doi, pdf)
- Olver, 2001: Joint invariant signatures (doi, pdf, slides)
- Calabi, Olver, et al, 1998: Differential and numerically invariant signature curves applied to object recognition (doi, pdf)
Invariants in science: