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| Paper IPM / M / 2349 |
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| Abstract: | |
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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 Hn ∩
Ho ≠ {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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