For more information about this meeting, contact Sergei Tabachnikov, Flossie Dunlop, Mari Royer.

Title: | Signatures of Hermitian forms and unitary representations |

Seminar: | Department of Mathematics Colloquium |

Speaker: | David Vogan, MIT |

Abstract: |

Suppose G is compact group. The representations of G - the possible ways of realizing G as group of matrices - provide a powerful and convenient way to organize the investigation of a wide variety of
problems involving symmetry under G.
When G is noncompact, there may be no such realizations using finite matrices, and those involving infinite matrices are too general to be useful. Stone, von Neumann, Wigner, and Gelfand realized in the 1930s that replacing finite matrices by unitary operators on Hilbert spaces provided a happy medium: that any group could be realized by such operators, but that the realizations could still be controlled in
interesting examples.
Gelfand's "unitary dual problem" asks for a list of all the realizations of a given G as unitary operators. I will describe recent work of Jeff Adams' research group "Atlas of Lie groups and representations" on an algorithm for solving this problem when G is simple Lie group. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 01 / 29 / 2009 |

Time: | 04:00pm - 05:00pm |