Multiplicity-free Kronecker products of characters of the symmetric   groups
  We provide a classification of multiplicity-free inner tensor products of irreducible characters of symmetric groups, thus confirming a conjecture of Bessenrodt. Concurrently, we classify all multiplicity-free inner tensor products of skew characters of the symmetric groups. We also provide formulae for calculating the decomposition of these tensor products. 
Christine Bessenrodt and Christopher Bowman
math.RT math.CO