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Paper   IPM / M / 2349
School of Mathematics
  Title:   Nonreduced extended affine Weyl groups
  Author(s):  S. Azam
  Status:   Published
  Journal: J. Algebra
  Vol.:  269
  Year:  2003
  Pages:   508-527
  Supported by:  IPM
In this paper we study the structure of the Weyl groups of nonreduced extended affine root systems. We show that similar to the case of reduced types, an extended affine Weyl group W of type BCl is semidirect product of a finite Weyl group W (of type Bl) and a Heisenberg-like normal subgroup H which is also a characteristic subgroup of W. Moreover, H is of the form H = Hη H0, where both Hη and H0 are normal subgroups of H with HnHo ≠ {1}, Hn is naturally isomorphic to the root lattice of a finite root system of type BCl. Furthermore, the semidirect product of W and Hn is isomorphic to the Weyl group of a Kac-Moody affine sub root system of R of type BCl.

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