Bulg. J. Phys. vol.35 no.s1 (2008), pp. 335-351

Composition Series for Representations of the Generalized Lorentz Group Associated with a Cone

G.F. Helminck1, A.V. Opimakh2
1Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
2Orienburg State Pedagogical University, Sovetskaya street 19, Orienburg, Russia
Abstract. Consider the cone C = {x is a member of Rn | -x12+x22 + ... + xn2 = 0, x1 > 0}. The group G := SO0(1, n-1) acts through its natural action on Rn on C. This action of G induces an action of G on the differential forms of degree one. In this paper we describe the composition series of G-invariant subspaces of these differential forms that are homogeneous along rays of the cone.

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