Irreducible unitary representations with non-zero relative Lie algebra cohomology of a Lie group of type f4(4)

Abstract

In this article, we have determined the irreducible unitary representations with non-zero relative Lie algebra cohomology and Poincare polynomials of cohomologies of these representations for a connected Lie group G with Lie algebra f4(4). We have also determined a necessary and sufficient condition for these representations to be discrete series representations and identified the discrete series representations and Borel-de Siebenthal discrete series representations among the irreducible unitary representations of G with non-zero relative Lie algebra cohomology.