A formula for the Kronecker products of Schur functions of hook shapes (Q1825272)

The question of how to decompose the tensor product of two irreducible characters of the finite symmetric groups is still open and appears to be very difficult. It is equivalent to decomposing the Kronecker product of Schur functions. The author gives a solution for the product of characters corresponding to hook shapes. This has also been done by Lascoux and by Gessel, but here it is shown that the multiplicities are 0, 1 or 2.