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On Two Presentations of the Affine Weyl Groups of Classical Types

✍ Scribed by Jian-yi Shi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
154 KB
Volume
221
Category
Article
ISSN
0021-8693

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✦ Synopsis

The main result of the paper is to get the transition formulae between the alcove form and the permutation form of w ∈ W a , where W a is an affine Weyl group of classical type. 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 compared with that in J. Y. Shi ( J. London Math. Soc. 35 (1987), 42-55). As applications, we give an affirmative answer to a conjecture of H. Eriksson and K. Eriksson (preprint, 1998) concerning the characterization of the inverse table of w ∈ W a ; we also describe the number Ο€ s w in terms of the permutation form of w ∈ W a .

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