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Lie Groups and Representation Theory Seminar

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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
[ 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.

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