Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896188 | Journal of Algebra | 2018 | 14 Pages |
Abstract
Given a rank n irreducible finite reflection group W, the W-invariant polynomial functions defined in Rn can be written as polynomials of n algebraically independent homogeneous polynomial functions, p1(x),â¦,pn(x), called basic invariant polynomials. Their degrees are well known and typical of the given group W. The polynomial p1(x) has the lowest degree, equal to 2. It has been proved that it is possible to choose all the other nâ1 basic invariant polynomials in such a way that they satisfy a certain system of differential equations, including the Laplace equations â³pa(x)=0, a=2,â¦,n, and so are harmonic functions. Bases of this kind are called canonical. Explicit formulas for canonical bases of invariant polynomials have been found for all irreducible finite reflection groups, except for those of types E6, E7 and E8. Those for the groups of types E6, E7 and E8 are determined in this article.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Vittorino Talamini,