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4 papers · 2 filters
Computing Vergne Polarizing Subalgebras
Vignon Oussa
According to Kirillov's theory, the construction of a unitary irreducible representation of a nilpotent Lie group requires a precise computation of some polarizing subalgebra subor…
Unitary Representations of Lattices of Free Nilpotent Lie Groups of Step-Two
Vignon Oussa
Using a theorem proved by Bekka and Driutti, we show that if is a freely generated nilpotent Lie algebra of step-two, then almost every irreducible representation of…
Sampling Theorems for Some Two-Step Nilpotent Lie Groups
Vignon Oussa
Let be a simply connected, connected nilpotent Lie group with the following assumptions. Its Lie Lie algebra is an -dimensional vector space over the reals. M…
Regular Representations of Time-Frequency Groups
Azita Mayeli, Vignon Oussa
In this paper, we study the Plancherel measure of a class of non-connected nilpotent groups which is of special interest in Gabor theory. Let be a time-frequency group. More pr…