Poincaré series of the Weyl groups of the elliptic root systems \(A_1^{(1,1)}\), \(A_1^{(1,1)^*}\) and \(A_2^{(1,1)}\).

zbMath1047.20030MaRDI QIDQ1408254

Tadayoshi Takebayashi

Publication date: 15 September 2003

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

zbMATH Keywords

Poincaré serieselliptic Weyl groupselliptic root systems

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Basic hypergeometric functions associated with root systems (33D67)

Related Items (5)

The growth series of the 2-extended affine Weyl group of type \(A_2^{(1,1)}\). ⋮ The \(q\)-Eulerian distribution of the elliptic Weyl group of type \(A_1^{(1,1)}\). ⋮ Gröbner-Shirshov bases of some Weyl groups ⋮ The Poincaré series of the central extension \(\widetilde W\) of the elliptic Weyl group of type \(A_1^{(1,1)}\). ⋮ The growth series of the \(n\)-extended affine Weyl group of type \(A_1\).

Cites Work

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• Extended affine root systems. II: Flat invariants
• Extended affine root systems. I: Coxeter transformations
• Extended affine root systems. III: Elliptic Weyl groups
• The Poincaré series of a Coxeter group
• Relations of the Weyl groups of extended affine root systems \(A_l^{(1,1)}\), \(B_l^{(1,1)}\), \(C_l^{(1,1)}\), \(D_l^{(1,1)}\)
• The orders of the finite Chevalley groups
• On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups

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