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Paper IPM / M / 2349  


Abstract:  
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 BC_{l} is semidirect product of a finite Weyl group
W (of type B_{l}) and a Heisenberglike normal subgroup
H which is also a characteristic subgroup of W.
Moreover, H is of the form H = H_{η}
H_{0}, where both H_{η} and H_{0}
are normal subgroups of H with H_{n} ∩
H_{o} ≠ {1}, H_{n} is naturally
isomorphic to the root lattice of a finite root system of type
BC_{l}. Furthermore, the semidirect product of W and
H_{n} is isomorphic to the Weyl group of a KacMoody
affine sub root system of R of type BC_{l}.
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