Exterior Algebra Structure for Relative Invariants of Reflection Groups

Details Exterior Algebra Structure for Relative Invariants of Reflection Groups Exterior Algebra Structure for Relative Invariants of Reflection Groups

2009-03-09

arxiv.org/abs/0903.1586v2

Mathematics

Group Theory

26 pages

Scientific paper

Let $G$ be a reflection group acting on a vector space $V$ (over a field with zero characteristic). We denote by $S(V^*)$ the coordinate ring of $V$, by $M$ a finite dimensional $G$-module and by $\chi$ a one-dimensional character of $G$. In this article, we define an algebra structure on the isotypic component associated to $\chi$ of the algebra $S(V^*) \otimes \Lambda(M^*)$. This structure is then used to obtain various generalizations of usual criterions on regularity of integers.

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