Mathematics – Group Theory
Scientific paper
2009-07-27
Mathematics
Group Theory
accepted for publication in the Journal of Group Theory
Scientific paper
A Gelfand model for a finite group $G$ is a complex linear representation of $G$ that contains each of its irreducible representations with multiplicity one. For a finite group $G$ with a faithful representation $V$, one constructs a representation which we call the polynomial model for $G$ associated to $V$. Araujo and others have proved that the polynomial models for certain irreducible Weyl groups associated to their canonical representations are Gelfand models. In this paper, we give an easier and uniform treatment for the study of the polynomial model for a general finite Coxeter group associated to its canonical representation. Our final result is that such a polynomial model for a finite Coxeter group $G$ is a Gelfand model if and only if $G$ has no direct factor of the type $W(D_{2n}), W(E_7)$ or $W(E_8)$.
Garge Shripad M.
Oesterle Joseph
No associations
LandOfFree
On Gelfand models for finite Coxeter groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Gelfand models for finite Coxeter groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Gelfand models for finite Coxeter groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-245947