Symplectic Mackey Theory
Speaker: Francois Ziegler, Georgia Southern University
Abstract: When a Lie group G has a closed normal subgroup N, the â€œMackey Machineâ€ breaks down the classification of its irreducible representations into two smaller problems: a) find the irreducible representations of N; b) find the irreducible projective representations of certain subgroups of G/N. The desired classification often follows inductively. Key parts of this machine are 1) the â€œinducing constructionâ€ (building representations of G out of those of its subgroups); 2) the â€œimprimitivity theoremâ€ (characterizing the range of the inducing construction); 3) a â€œtensoringâ€ construction (combining objects of types a) and b) above). Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup, thus introducing a purely symplectic geometrical analog of 1); and the question arose whether analogs of 2) and 3) could be found and built into an effective â€œsymplectic Mackey Machineâ€. In this talk I will describe a complete solution to this problem, obtained recently.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm