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Session III.6 - Symbolic Analysis

Monday, June 19, 14:00 ~ 14:30

Computing the fundamental invariants and equivariants of a finite group

Evelyne Hubert

Inria Méditerranée, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

For a finite group, we present three algorithms 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. \url{}

Joint work with Erick Rodiguez Bazan.

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