Symplectic Mackey Theory

Meeting Details

For more information about this meeting, contact Mathieu Stiénon, Ping Xu, Nigel Higson.

Speaker: Francois Ziegler, Georgia Southern University

Abstract: When a Lie group G has a closed normal subgroup N, the “Mackey Machine” 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 “inducing construction” (building representations of G out of those of its subgroups); 2) the “imprimitivity theorem” (characterizing the range of the inducing construction); 3) a “tensoring” 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 “symplectic Mackey Machine”. In this talk I will describe a complete solution to this problem, obtained recently.

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Room Reservation Information

Room Number: 106 McAllister

Date: 03/17/2015

Time: 2:30pm - 3:30pm