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Computing fundamental invariants and equivariants of a finite group action

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EMGW02 - Applied and computational algebraic geometry

For a finite group, we present an algorithm to compute a generating set of invariant simultaneously to generating sets of basic equivariants, i.e., equivariants for the irreducible representations of the group. The main novelty resides in the exploitation of the orthogonal complement of the ideal generated by invariants; Its symmetry adapted basis delivers the fundamental equivariants. Fundamental equivariants allow to assemble symmetry adapted bases of polynomial spaces of higher degrees, and these are essential ingredients in exploiting and preserving symmetry in computations. They appear within algebraic computation and beyond, in physics, chemistry and engineering. This is joint work with Erick Rodiguez Bazan published as: E. Hubert &  E. Rodriguez Bazan. Algorithms for fundamental invariants and equivariants (of finite groups);  Mathematics of Computation, volume 91 number 337 pages 2459-2488 (2022) [doi:10.1090/mcom/3749]

This talk is part of the Isaac Newton Institute Seminar Series series.

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