On two presentations of the affine Weyl groups of the classical types


Jian-yi Shi


Research Report 98-3
Date: 4 February 1998, revised 28 March 1998


The main result of the paper is to get the transition formulae between the alcove form and the permutation form of an element w in Wa, where Wa is an affine Weyl group of type B~m (m > 2), C~n (n > 1) or D~k (k > 3). On the other hand, we get a new characterization for the alcove form of an affine Weyl group element which has a much simpler form comparing with that in [10]. Our results give an affirmative answer to a conjecture of H. Eriksson and K. Eriksson in [4] concerning the characterization of the inverse table of an element w in Wa.

Key phrases

affine Weyl groups. alcove form. permutation form. transition formulae.

AMS Subject Classification (1991)

Primary: 20H15
Secondary: 20F55


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