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
@article{JAC_2005__22_1_a0,
author = {Shepler, Anne V.},
title = {Generalized exponents and forms},
journal = {Journal of Algebraic Combinatorics},
pages = {115--132},
publisher = {mathdoc},
volume = {22},
number = {1},
year = {2005},
language = {en},
url = {https://geodesic-test.mathdoc.fr/item/JAC_2005__22_1_a0/}
}
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/