Generalized Exponents and Forms |
| |
Authors: | Anne V Shepler |
| |
Institution: | (1) Mathematics Department, University of North Texas, Denton, Texas, U.S.A. |
| |
Abstract: | 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. |
| |
Keywords: | reflection group invariant theory generalized exponents Coxeter group fake degree hyperplane arrangement derivations |
本文献已被 SpringerLink 等数据库收录! |