Journal of Lie Theory Volume 6 (1996) 53–68 ◯^{C} 1996 Heldermann Verlag

The Weyl group as fixed point set of smooth involutions

Filippo De Mari

Communicated by G. Mauceri

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 exp i𝔞. The Weyl group is either X, or the fixed point set of the involutions defined on X by special elements of order 4 in exp i𝔞.

Filippo De Mari Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy demari@dima.unige.it

Received January, 16 1996 and in final form April, 26 1996

ISSN 0949–5932 / $2.50 ◯^{C} Heldermann Verlag