For more information about this meeting, contact Nigel Higson, Stephanie Zerby.

Title: | Generalized exponents, family algebras and representations with simple spectrum |

Seminar: | Department of Mathematics Colloquium |

Speaker: | Alexandre Kirillov, University of Pennsylvania |

Abstract: |

In representation theory there are several "evergreen" subjects such as symmetric functions, multiplicity of weights, tensor invariants, etc. One of such subject, less known among non-experts, is the theory of generalized exponents, introduced by Kostant half a century ago and still resisting all endeavors towards explicit computation. The collection of generalized exponents is the so-called q-analogue of the multiplicity of the zero weight. As one possible approach to the problem, I introduced in 2000 the notion of a family algebra associated to any irreducible representation of a simple Lie algebra. The structure of these algebras is closely related to generalized exponents. For representations with simple spectrum, family algebras have relatively a simple structure, and this allows to compute explicitly generalized exponents for many irreducible representations. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 01 / 31 / 2013 |

Time: | 03:35pm - 04:25pm |