Small Black Hole Constituents and Horizontal Symmetry

By exploiting the role of the horizontal symmetry SL(2,R), we extend the analysis and classification of two-centered extremal black hole charge configurations to the case of "small" single-centered constituents. These latter are seen to decrease the number of independent horizontal-invariant polynomials from four to one, depending on the rank of the charge orbit supporting each of the two centers. Within U-duality groups of type E7, both reducible and irreducible symmetric supergravity models in four space-time dimensions are considered, thus encompassing N = 2 and N = 8 theories.