The growth series of the $n$-extended affine Weyl group of type $A_1$
Tadayoshi Takebayashi
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 81, Number 3
(2005), 51-56.
Abstract
$N$-extended affine Weyl groups are Weyl groups associated to $n$-extended affine root systems introduced by K. Saito [1]. We calculate the growth series of the n-extended affine Weyl group of type $A_1$ with a generator system of an $n$-toroidal sense.
First Page:
Show
Hide
Primary Subjects:
20D30
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pja/1116442037
Mathematical Reviews number (MathSciNet): MR2128932
Zentralblatt MATH identifier: 1084.20028
Digital Object Identifier: doi:10.3792/pjaa.81.51
References
K. Saito, Extended affine root systems. I. Coxeter transformations, Publ. Res. Inst. Math. Sci. 21 (1985), no. 1, 75--179.
Mathematical Reviews (MathSciNet): MR780892
K. Saito and T. Takebayashi, Extended affine root systems. III. Elliptic Weyl groups, Publ. Res. Inst. Math. Sci. 33 (1997), no. 2, 301--329.
Mathematical Reviews (MathSciNet): MR1442503
R. P. Stanley, Enumerative combinatorics. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Adv. Books Software, Monterey, CA, 1986.
Mathematical Reviews (MathSciNet): MR847717
M. Wakimoto, Poincaré series of the Weyl group of elliptic Lie algebras $A_1^(1,1)$ and $A_1^(1,1)*$, q-alg/9705025.
T. Takebayashi, Poincaré series of the Weyl groups of the elliptic root systems $A_1^(1,1),\ A_1^(1,1)*$ and $A_2^(1,1)$, J. Algebraic Combin. 17 (2003), no. 3, 211--223.
Mathematical Reviews (MathSciNet): MR2001669
Digital Object Identifier: doi:10.1023/A:1025081404009
Proceedings of the Japan Academy, Series A, Mathematical Sciences
