Kostant's generating functions, Ebeling's theorem and McKay's observation relating the Poincare series

Details Kostant's generating functions, Ebeling's theorem and McKay's observation relating the Poincare series Kostant's generating functions, Ebeling's theorem and McKay's observation relating the Poincare series

2006-08-20

arxiv.org/abs/math/0608500v1

Mathematics

Representation Theory

22 pages, 1 figure

Scientific paper

We generalize B. Kostant's construction of generating functions to the case of multiply-laced diagrams and we prove for this case W. Ebeling's theorem which connects the Poincare series [P_G(t)]_0 and the Coxeter transformations. According to W. Ebeling's theorem [P_G(t)]_0 = \frac{X(t^2)}{\tilde{X}(t^2)}, where X is the characteristic polynomial of the Coxeter transformation and \tilde{X} is the characteristic polynomial of the corresponding affine Coxeter transformation. We prove McKay's observation relating the Poincare series [P_G(t)]_i: (t+t^{-1})[P_G(t)]_i = \sum\limits_{i \leftarrow j}[P_G(t)]_j, where j runs over all vertices adjacent to i.

Affiliated with

Also associated with

No associations

Rating

Kostant's generating functions, Ebeling's theorem and McKay's observation relating the Poincare series 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 Kostant's generating functions, Ebeling's theorem and McKay's observation relating the Poincare series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Kostant's generating functions, Ebeling's theorem and McKay's observation relating the Poincare series will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-226603