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

## Author

**Jian-yi Shi**

## Status

Research Report 98-3

Date: 4 February 1998, revised 28 March 1998

## Abstract

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

## Content

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1998-3.dvi (81kB)

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