Vol. 107, No. 2, 1983

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Products of positive reflections in real orthogonal groups

Dragomir Z. Djokovic

Vol. 107 (1983), No. 2, 341–348

Let O(f) be the orthogonal group of a symmetric bilinear form f defined on a finite-dimensional real vector space V . If f is indefinite then O(f) has two conjugacy classes of reflections, one of which consists of so called positive reflections. We denote by G+ the subgroup of O(f) generated by all positive reflections. In this paper we describe this subgroup and solve the length problem in G+ with respect to the distinguished set of generators. When f is non-degenerate this problem was solved by J. Malzan. Our proof (in the case of arbitrary f) is shorter and completely different from his proof.

Mathematical Subject Classification 2000
Primary: 20H15
Secondary: 51N30
Received: 10 September 1981
Published: 1 August 1983
Dragomir Z. Djokovic