Classification of Irreducible (𝔤, 𝔨)-Modules Associated to the Ideals of Minimal Nilpotent Orbits for Simple Lie Groups of TypeA

Abstract

AbstractWe classify completely prime primitive ideals whose associated varieties are the closure of the minimal nilpotent coadjoint orbit for $\mathfrak {g}=\mathfrak {s}\mathfrak {l}(n,\mathbb {C})$ and classify irreducible $(\mathfrak {g},\mathfrak {k})$-modules, which have those ideals as annihilators. Moreover, we irreducibly decompose them as $\mathfrak {k}$-modules.