https://hdl.handle.net/1721.1/18160 Thu, 09 Apr 2026 16:25:24 GMT 2026-04-09T16:25:24Z https://hdl.handle.net/1721.1/29468 Strictly small representations and a reduction theorem for the unitary dual Salamanca-Riba, Susana A.; Vogan, David To any irreducible unitary representation X of a real reductive Lie group we associate in a canonical way, a Levi subgroup Gsu and a representation of this subgroup. Assuming a conjecture of the authors on the infinitesimal character of X, we show that X is cohomologically induced from a unitary representation of the subgroup Gsu. This subgroup is in some cases smaller than the subgroup Gu that the authors attached to X in earlier work. In those cases this provides a further reduction to the classification problem. First published in Representation Theory in Vol 5, 2001. Published by the American Mathematical Society. Mon, 01 Jan 2001 00:00:00 GMT https://hdl.handle.net/1721.1/29468 2001-01-01T00:00:00Z https://hdl.handle.net/1721.1/29467 Functions on the model orbit in E8 Adams, J.; Huang, J.; Vogan, David We decompose the ring of regular functions on the unique coadjoint orbit for complex E8 of dimension 128, finding that every irreducible representation appears exactly once. This confirms a conjecture of McGovern. We also study the unique real form of this orbit. First published in Representation Theory in Vol.2,1998. Published by the American Mathematical Society. Fri, 01 Jan 1988 00:00:00 GMT https://hdl.handle.net/1721.1/29467 1988-01-01T00:00:00Z