Poincaré series of the Weyl group of elliptic Lie algebras $A^{(1,1)}_1$ and $A^{(1,1) \ast}_1$

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In this note, we calculate the Poincaré series of elliptic Weyl groups of type $A^{(1,1)}_1$ and $A^{(1,1) \ast}_1$ and show that they have a simple expression.
9 pages, amslatex. A reference on the Bruhat-Tits buildings is added.

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