Poincaré Series of the Weyl Groups of the Elliptic Root Systems A 1 (1,1), A 1 (1,1)* and A 2 (1,1)
Tadayoshi Takebayashi
DOI: 10.1023/A:1025081404009
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.
Pages: 211–223
Keywords: Poincaré series; elliptic root system; elliptic Weyl group
Full Text: PDF
References
1. N. Bourbaki Groupes et algebr`es de Lie, Ch. 4-6, Hermann, Paris, 1968; Mason, Paris, 1981.
2. J.E. Humphreys, “Reflection groups and Coxeter groups,” Cambridge Studies in Advanced Math. Cambridge University Press, 1990, vol. 29.
3. 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.
4. I.G. Macdonald, “The Poincaré series of a Coxeter group,” Math. Ann. 199 (1972), 161-174.
5. K. Saito, “Extended affine root systems I,” Publ. RIMS, Kyoto Univ. 21 (1985), 75-179. POINCAR É SERIES OF THE WEYL GROUPS 223
6. K. Saito, “Extended affine root systems II,” Publ. RIMS, Kyoto Univ. 26 (1990), 15-78.
7. K. Saito and T. Takebayashi, “Extended affine root systems III,” Publ. RIMS, Kyoto Univ. 33 (1997), 301-329.
8. L. Solomon, “The orders of the finite Chevalley groups,” Journal of Algebra 3 (1966), 376-393.
9. T. Takebayashi “Relations of the Weyl groups of extended affine root systems A(1,1), B(1,1), C(1,1), D(1,1),” l l l l Proc. Japan Acad. 71(6) (1995), A123-124.
10. M. Wakimoto, “Poincaré series of the Weyl group of elliptic Lie algebras A(1,1) and A(1,1)* ,” q-alg/9705025. 1
2. J.E. Humphreys, “Reflection groups and Coxeter groups,” Cambridge Studies in Advanced Math. Cambridge University Press, 1990, vol. 29.
3. 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.
4. I.G. Macdonald, “The Poincaré series of a Coxeter group,” Math. Ann. 199 (1972), 161-174.
5. K. Saito, “Extended affine root systems I,” Publ. RIMS, Kyoto Univ. 21 (1985), 75-179. POINCAR É SERIES OF THE WEYL GROUPS 223
6. K. Saito, “Extended affine root systems II,” Publ. RIMS, Kyoto Univ. 26 (1990), 15-78.
7. K. Saito and T. Takebayashi, “Extended affine root systems III,” Publ. RIMS, Kyoto Univ. 33 (1997), 301-329.
8. L. Solomon, “The orders of the finite Chevalley groups,” Journal of Algebra 3 (1966), 376-393.
9. T. Takebayashi “Relations of the Weyl groups of extended affine root systems A(1,1), B(1,1), C(1,1), D(1,1),” l l l l Proc. Japan Acad. 71(6) (1995), A123-124.
10. M. Wakimoto, “Poincaré series of the Weyl group of elliptic Lie algebras A(1,1) and A(1,1)* ,” q-alg/9705025. 1