Geodesic
Generalized exponents and forms
Journal of Algebraic Combinatorics, Tome 22 (2005) no. 1, pp. 115-132.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: We consider generalized exponents of a finite reflection group acting on a real or complex vector space V. These integers are the degrees in which an irreducible representation of the group occurs in the coinvariant algebra. A basis for each isotypic component arises in a natural way from a basis of invariant generalized forms. We investigate twisted reflection representations ( V tensor a linear character) using the theory of semi-invariant differential forms. Springer's theory of regular numbers gives a formula when the group is generated by dim V reflections. Although our arguments are case-free, we also include explicit data and give a method (using differential operators) for computing semi-invariants and basic derivations. The data give bases for certain isotypic components of the coinvariant algebra.
Mots-clés : keywords reflection group, invariant theory, generalized exponents, Coxeter group, fake degree, hyperplane arrangement, derivations 
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Shepler, Anne V. Generalized exponents and forms. Journal of Algebraic Combinatorics, Tome 22 (2005) no. 1, pp. 115-132. https://geodesic-test.mathdoc.fr/item/JAC_2005__22_1_a0/