Nonreduced extended affine Weyl groups

[摘要] 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 B-l) and a Heisenberg-like normal subgroup H which is also a characteristic subgroup of W. Moreover, H is of the form H = HnH0, where both H-n and H-0 are normal subgroups of H with H-n boolean AND H-0 not equal {1}, H-n is naturally isomorphic to the root lattice of a finite root system of type BCl. Furthermore, the semidirect product of V and H-n is isomorphic to the Weyl group of a Kac-Moody affine subroot system of R of type BCl. (C) 2003 Published by Elsevier Inc.

[发布日期] 2003-11-15