Meeting Details

Title: "Kirillov's Orbit Method" Ph.D. Oral Comprehensive Examination Ehssan Khanmohammadi, Adviser: Nigel Higson, Penn State http:// The orbit method was introduced in 1960s by Kirillov to characterize the unitary irreducible representations of nilpotent Lie groups by studying the action of Lie groups on the dual space of their Lie algebras. The theory shows that the irreducible unitary representations of a nilpotent Lie group $G$ are in one-to-one correspondence with the coadjoint orbits in $\mathfrak g^*$, and that each such representation is induced, in the sense of Mackey, by a one-dimensional representation. After a quick tour of preliminary material we introduce some of the key concepts of the orbit method philosophy, and finally we shall attempt to give a direct and polarization-free argument for the positivity of the character of nilpotent Lie groups choosing Kirillov's Character formula as the definition of a character.