ON MINIMAL FAITHFUL REPRESENTATIONS OF NILRADICALS

Abstract

In this work we consider 2-step nilradicals of parabolic subalgebras of the simple Lie algebra $A_n$ and describe a new family of faithful nil-representations of the nilradicals $\mathfrak{n}_{a,c}$, $a,c\in\mathbb{N}$. We obtain a sharp upper bound for the minimal dimension $\mu(\mathfrak{n}_{a,c})$ and for several pairs $(a,c)$ we obtain $\mu(\mathfrak{n}_{a,c})$.