[ Seminar 2018 | Past Seminars | Related conferences etc. ]

Speaker: | Ali Baklouti (Faculté des Sciences de Sfax) |

Date: | Dec 3 (Mon), 2018, 17:00-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Title: | Monomial representations of discrete type and differential operators |

Abstract: [ pdf ] | Let $G$ be an exponential solvable Lie group and $¥tau$ a monomial representation of $G$, an induced representation from a connected closed subgroup of $G$ of a unitary character. It is well known that $¥tau$ disintegrates into irreducible factors and the multiplicities of each isotypic component are explicitly determined. In the case where $G$ is nilpotent, these multiplicities are either finite or infinite almost everywhere, with respect to the disintegration's measure. We associate to $¥tau$ an algebra of differential operators and it is shown that in the nilpotent case, the commutativity of this algebra is equivalent to the finiteness of the multiplicities of $¥tau$. In the exponential case, we define the notion of monomial representation of discrete type. In this case, we show that such an equivalence does not hold and this answers a question posed by M. Duflo. This is a joint work with H. Fujiwara and J. Ludwig. |

- Lie Groups and Representation Theory Seminar [ 1987 | 1988 | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 ] (academic year)
- Lie Groups and Representation Theory Seminar
- Lie Groups and Representation Theory Seminar [ 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 ]
- Working Seminar on Integral Geometry at RIMS, Kyoto University [ 2004.10-2005.02 ]

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