From arXiv

In our previous paper math.QA/0409261, we defined a deformation of the group algebra of the group of even elements of a Coxeter group W, and showed that it is flat for all values of parameters if and only if all the rank 3 parabolic subgroups of W are infinite. In this paper, we study what happens in the general case. Then the deformation is flat only for some values of parameters, and the set of all such values is called the flatness locus. The main result of the paper is an explicit description of the this flatness locus as a scheme over Z. More specifically, we show that this scheme is the intersection of the flatness loci for the subalgebras corresponding to parabolic subgroups of rank 3. The latter are determined by solving the rigid multiplicative Deligne-Simpson problem. We also define additive analogs of our algebras and study their properties.

Simplify

Updated on October 31, 2006

Copy BibTeX

Edited 2 times

Loading...

Summary

There is no AI-powered summary yet, because we do not have a budget to generate summaries for all articles.

1. Buy subscription

We will thank you for helping thousands of people to save their time at the top of the generated summary.

If you buy our subscription, you will be able to summarize multiple articles.

See an example

Pay $8

≈10 summaries

Pay $32

≈60 summaries

2. Share on socials

If this article gets to top-5 in trends, we'll summarize it for free.

Copy link