Variations of the Poincaré series for affine Weyl groups and q-analogues of Chebyshev polynomials

Eric Marberg, Graham White

Let $(W,S)$ be a Coxeter system and write $P_W(q)$ for its Poincaré series. Lusztig has shown that the quotient $P_W(q^2)/P_W(q)$ is equal to a certain power series $L_W(q)$, def…