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Journal of the London Mathematical Society 1987 s2-35(1):42-55; doi:10.1112/jlms/s2-35.1.42
© 1987 by London Mathematical Society
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© Oxford University Press

Alcoves Corresponding to an Affine Weyl Group

Jian-Yi Shi

Department of Mathematics, East China Normal University Shanghai, China

In this paper, I study the alcoves of a Euclidean space E corresponding to an affine Weyl group Wa I give the coordinate form of an alcove of E and establish an explicit correspondence between the elements of Wa and the alcoves of E. In particular, I characterize an alcove by a FE-tuple over Z subject to certain conditions, where FE is the root system determined by Wa.


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