https://hdl.handle.net/1721.1/18161 2026-04-10T08:20:12Z 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. 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. 1988-01-01T00:00:00Z