Based on an idea in [Gan-Savin, Represent. Theory (2005)], we give a classification of minimal representations of connected simple real Lie groups not of type A. Actually, we prove that there exist no new minimal representations up to infinitesimal equivalence. Mathematics Subject Classification 2010: 22E46.
We 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.
We classify completely prime primitive ideals whose associated varieties are the closure of the minimal nilpotent orbit of g = sl(n, C), and classify irreducible (g, k)-modules which have those ideals as annihilators. Moreover, we irreducibly decompose them as k-modules. Mathematics Subject Classification 2010: 22E46.
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