We show that the Weyl group W = M′/M of a noncompact semisimple Lie group is obtained by taking fixed point sets of smooth involutions in K/M . More precisely, one considers first the fixed point set X of the involutions defined on K/M by the elements of order 2 in expia. The Weyl group is either X , or the fixed point set of the involutions defined on X by special elements of order 4 in expia.
The Weyl group as fixed point set of smooth involutions
DE MARI CASARETO DAL VERME, FILIPPO
1996-01-01
Abstract
We show that the Weyl group W = M′/M of a noncompact semisimple Lie group is obtained by taking fixed point sets of smooth involutions in K/M . More precisely, one considers first the fixed point set X of the involutions defined on K/M by the elements of order 2 in expia. The Weyl group is either X , or the fixed point set of the involutions defined on X by special elements of order 4 in expia.
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