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Saturation rank for nilradical of parabolic subalgebras in Type A
Yang Pan
https://arxiv.org/abs/2405.01956 https://arxiv.org/pdf/240…

Saturation rank for nilradical of parabolic subalgebras in Type A
Let $\mfp(d)$ be a standard parabolic subalgebra of $\mfsl_{n+1}(K)$ and $\mfu$ be the corresponding nilradical defined over an algebraically closed field $K$ of characteristic $p>0$. We construct a finite connected quiver $Q(d)$, through which we provide a combinatorial characterization of the centralizer $c_{\mfu}(x(d))$ of the Richardson element $x(d)$. We specifically focus on the centralizer when the levi factor of $\mfp(d)$ is determined by either one or two simple roots. This allows us t…