Mathematics – Group Theory
Scientific paper
2006-03-23
Mathematics
Group Theory
Slightly revised version, to appear in Trans. Amer. Math. Soc.
Scientific paper
We study symmetries enjoyed by the polynomials enumerating non-degenerate flags in finite vector spaces, equipped with a non-degenerate alternating bilinear, hermitian or quadratic form. To this end we introduce Igusa-type rational functions encoding these polynomials and prove that they satisfy certain functional equations. Some of our results are achieved by expressing the polynomials in question in terms of what we call parabolic length functions on Coxeter groups of type $A$. While our treatment of the orthogonal case exploits combinatorial properties of integer compositions and their refinements, we formulate a precise conjecture how in this situation, too, the polynomials may be described in terms of parabolic length functions.
Klopsch Benjamin
Voll Christopher
No associations
LandOfFree
Igusa-type functions associated to finite formed spaces and their functional equations 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 Igusa-type functions associated to finite formed spaces and their functional equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Igusa-type functions associated to finite formed spaces and their functional equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-305945