Poincaré series of the Weyl group of elliptic Lie algebras $A_1^{(1,1)}$ and $A_1^{(1,1)\ast }$

Abstract

In this note, we calculate the Poincaré series of elliptic Weyl groups of type $A_1^{(1,1)}$ and $A_1^{(1,1)\ast }$ and show that they have a simple expression.

arXiv comment9 pages, amslatex. A reference on the Bruhat-Tits buildings is added.