Abstract
We calculate the Poincaré series of the elliptic Weyl group W(A 2 (1,1)), which is the Weyl group of the elliptic root system of type A 2 (1,1). The generators and relations of W(A 2 (1,1)) have been already given by K. Saito and the author.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Bourbaki Groupes et algebrès de Lie, Ch. 4–6, Hermann, Paris, 1968; Mason, Paris, 1981.
J.E. Humphreys, “Reflection groups and Coxeter groups,” Cambridge Studies in Advanced Math. Cambridge University Press, 1990, vol. 29.
N. Iwahori and H. Matsumoto, “On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups,” Publ. Math. I.H.E.S. 25 (1965), 5–48.
I.G. Macdonald, “The Poincarè series of a Coxeter group,” Math. Ann. 199 (1972), 161–174.
K. Saito, “Extended affine root systems I,” Publ. RIMS, Kyoto Univ. 21 (1985), 75–179.
K. Saito, “Extended affine root systems II,” Publ. RIMS, Kyoto Univ. 26 (1990), 15–78.
K. Saito and T. Takebayashi, “Extended affine root systems III,” Publ. RIMS, Kyoto Univ. 33 (1997), 301–329.
L. Solomon, “The orders of the finite Chevalley groups,” Journal of Algebra 3 (1966), 376–393.
T. Takebayashi “Relations of the Weyl groups of extended affine root systems A (1,1) l , B (1,1) l , C (1,1) l , D (1,1) l ,” Proc. Japan Acad. 71(6) (1995), A123–124.
M. Wakimoto, “Poincarè series of the Weyl group of elliptic Lie algebras A1/(1,1) and A1/(1,1)*,” q-alg/9705025.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Takebayashi, T. Poincaré Series of the Weyl Groups of the Elliptic Root Systems A 1 (1,1), A 1 (1,1)* and A 2 (1,1) . Journal of Algebraic Combinatorics 17, 211–223 (2003). https://doi.org/10.1023/A:1025081404009
Issue Date:
DOI: https://doi.org/10.1023/A:1025081404009