Real orthogonal representation of real semisimple Lie group (Q687950)

The author discusses infinite dimensional real orthogonal representations of a real semisimple Lie group \(G\) mainly using the lowest \(K\)-type theory developed by D. Vogan. By using his results, one can classify irreducible orthogonal representations of \(G\) when the finite dimensional representations of \(G\) are self-dual.