  This is a continuation of arXiv:0903.0398 [math.RT]. Let g be a simple Lie
algebra. In this note, we provide simple formulae for the index of
sl(2)-subalgebras in the classical Lie algebras and a new formula for the index
of the principal sl(2). We also compute the difference, D, of the indices of
principal and subregular sl(2)-subalgebras. Our formula for D involves some
data related to the McKay correspondence for g. Using the index of
sl(2)-subalgebras of classical Lie algebras, we also obtain three series of
interesting combinatorial identities parameterised by partitions.

Representation Theory