arXiv subjects

Michel Duflo

Publications and source records attributed to Michel Duflo.

4 recordsLinked to original sources

arXiv2014

On compositions associated to Frobenius parabolic and seaweed subalgebras of $\mathrm{sl}_{n}(\Bbbk )$

By using a free monoid of operators on the set of compositions (resp. pairs of compositions), we establish in this paper a bijective correspondence between Frobenius standard parabolic (resp. seaweed) subalgebras and certain elements of this monoid. We prove via this correspondence a conjecture of one of the authors on the number of Frobenius standard parabolic (resp. seaweed) subalgebras of $\mathrm{sl}_{n}(\Bbbk )$ associated to compositions (resp. pairs of compositions) with $n-t$ parts (resp. parts in total).

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arXiv2011

Kirillov's formula and Guillemin-Sternberg conjecture

Let G be a connected reductive real Lie group, and H a compact connected subgroup. Harish-Chandra associates to a regular coadjoint admissible orbit M of G some unitary representations of G. Using the character formula for these representations, we show that the multiplicities of the restriction to H can be computed, under a suitable properness assumption, in terms of the fibers of the restriction map from M to the dual of the Lie algebra of H. In particular, this gives an alternate proof of a result of Paradan.

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arXiv2011

Algèbres de Lie quasi-réductives

We study the class of algebraic Lie algebras for which the generic stabilizer of the coadjoint action is reductive modulo the center.

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arXiv2007

Symmetric pairs and Gorelik elements

The second author gave a formula for the elements of the enveloping algebra of a Lie superalgebra defined by Gorelik under an appropriate unimodularity assumption. We show that this formula is a particular case of a formula for the Jacobian of the exponential map of a symmetric superspace.

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