R. Merris, Nonzero decomposable symmetrized tensors, Linear Algebra Appl. 17 (1977), 287-292. AMS Notices 23 (1976), A-66. Math. Reviews 58 #5889.

Let alpha and beta be partitions of the positive integer m. Let chi be the irreducible complex character of S_m corresponding to the partition alpha and lambda be the permutation character of S_m induced from the principal (identically 1) character on the Young subgroup of S_m corresponding to beta. It is shown that chi is a component of lambda if and only if alpha majorizes beta, confirming a conjecture of E. Snapper, Group characters and nonnegative integral matrices, J. Algebra 19 (1971), 520-535. As an application, let V be a vector space with a basis e1, e2, ... , en. Let z be the tensor product of some m of these basis vectors, chosen with replacement. Let z* be the corresponding decomposable symmetrized tensor afforded by S_m and chi. Then z* is nonzero if and only if alpha majorizes the "m-tuple of multiplicities" of z. Further applications to immanants can be found in publication 34. Subsequent work in this area is summarized in [R. Merris, Multilinear Algebra, Gordon & Breach, Amsterdam, 1997, pp 169-172]. Among the publications citing this article are: