Bachir Bekka

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math.RT2025

Canonical Commutation Relations: A quick proof of the Stone-von Neumann theorem and an extension to general rings

Bachir Bekka

Let $R$ be a (not necessary commutative) ring with unit, $d \geq 1$ an integer, and $I^»$ a unitary character of the additive group $(R, +) .$ A pair $(U, V)$ of unitary representations…

math.RT2024

The $L_{p}$ -dual space of a semisimple Lie group

Bachir Bekka

Let $G$ be a semisimple Lie group. We describe the irreducible representations of $G$ by linear isometries on $L_{p}$ -spaces for $p \in (1, + \infty)$ with $p \neq = 2.$ More precisely, we…

Canonical Commutation Relations: A quick proof of the Stone-von Neumann theorem and an extension to general rings

The Lp​-dual space of a semisimple Lie group

The $L_{p}$ -dual space of a semisimple Lie group