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The low energy spectrum of the ferromagnetic Kondo lattice model on a N-sitecomplete graph extended with on-site repulsion is obtained from the underlyingspl(2,1) algebra properties in the strong coupling limit. The ferromagneticground state is realized for 1 and N+1 electrons only. We identify the largedensity of states to be responsible for the suppression of the ferromagneticstate and argue that a similar situation is encountered in the Kagome,pyrochlore, and other lattices with flat bands in their one-particle density ofstates.Comment: 7 pages, 1 figur

spl (2,1) dynamical supersymmetry and suppression of ferromagnetism in flat-band double-exchange models