... Again, for the application of H to eλ , the only alteration to the right side of (6) would be a change of cλ to dλ One of the main aims of this paper is to deduce the form of Ωe l from that of Ωm ... called for When α = 2, the operator L is the Laplace Beltrami operator of differential geometry for GL(n, R) acting on cosets of the orthogonal group O(n) (see i.a [1, p 386], [2]) For α = the Jack ... symmetric functions pλ (for the definition of which see e.g [6, p 77], [4, p 23]) For the purposes of this paper, then, H and L differ by a constant, given in the second half of (3) This paper encompasses...