\(q\)-deformation of the group algebra \(k[\widehat W]\) associated to the elliptic root system \(A_l^{(1,1)}\) (\(l\geq 2\)). (English) Zbl 0957.20030

Takebayashi, Tadayoshi

Proc. Japan Acad., Ser. A 76, No. 3, 35-38 (2000).

Summary: In the case of elliptic root system \(A^{(1,1)}_l\) (\(l\geq 2\)), a \(q\)-deformation algebra of the hyperbolic extension of the elliptic Weyl group is constructed by using a representation according to Kazhdan-Lusztig.

MSC:

20G42	Quantum groups (quantized function algebras) and their representations
17B37	Quantum groups (quantized enveloping algebras) and related deformations
20F55	Reflection and Coxeter groups (group-theoretic aspects)

Keywords:

elliptic root systems; \(q\)-deformation algebras; hyperbolic extensions; elliptic Weyl groups

References:

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