## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### The growth series of the $n$-extended affine Weyl group of type $A_1$

#### 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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 3 (2005), 51-56.

Dates
First available in Project Euclid: 18 May 2005

https://projecteuclid.org/euclid.pja/1116442037

Digital Object Identifier
doi:10.3792/pjaa.81.51

Mathematical Reviews number (MathSciNet)
MR2128932

Zentralblatt MATH identifier
1084.20028

Subjects
Primary: 20D30: Series and lattices of subgroups

#### Citation

Takebayashi, Tadayoshi. The growth series of the $n$-extended affine Weyl group of type $A_1$. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 3, 51--56. doi:10.3792/pjaa.81.51. https://projecteuclid.org/euclid.pja/1116442037

#### References

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• K. Saito and T. Takebayashi, Extended affine root systems. III. Elliptic Weyl groups, Publ. Res. Inst. Math. Sci. 33 (1997), no. 2, 301–329.
• R. P. Stanley, Enumerative combinatorics. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Adv. Books Software, Monterey, CA, 1986.
• 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.