De Ali Baklouti
Let $G$ be a connected and simply connected nilpotent Lie group, $K$ an analytic subgroup of $G$ and $\pi$ an irreducible unitary representation of $G$ whose coadjoint orbit of $G$ is denoted by $\Omega(\pi)$. Let $\mathcal U(\mathfrak g)$ be the enveloping algebra of $\mathfrak g_{\mathbb C}$, $\mathfrak g$ designating the Lie algebra of $G$. We consider the algebra $D_{\pi}(G)^K\simeq (\mathcal U(\mathfrak g)/ \ker \pi)^K$ of the $K$-invariant elements of $\mathcal U(\mathfrak g)/ \ker \pi$. It turns out that this algebra is commutative if and only if the restriction $\pi|K$ of $\pi$ to $K$ has finite multiplicities (A. Baklouti–H. Fujiwara 2004). In this lecture, I will talk about the polynomial conjecture asserting that $D_\pi(G)^K$ is isomorphic to the algebra $\mathbb C[\Omega(\pi)]^K$ of $K$-invariant polynomial functions on $\Omega(\pi)$, provided that $\pi|K$ is of finite multiplicities. This is a joint work with H. Fujiwara and J. Ludwig.
De Salem Ben Said
De Patrick Delorme
De Salma Nasrin
De Genkai Zhang
De Andreas Juhl
De Reiko Miyaoka
De Ali Baklouti
De Yoshiki Oshima
De Dan Barbasch
De Kazuki Kannaka
De Jan Frahm
De Angela Pasquale
De Claudio Dappiaggi
De Alexander Strohmaier
De Hans Lindblad
