Tables of reductions of symmetrized inner products (“inner plethysms”) of ordinary irreducible representations of symmetric groups

Abstract

Decompositions of symmetrized inner products [ α ] ⊡ [ β ] [\alpha ] \boxdot [\beta ] of ordinary irreducible representations [ α ] [\alpha ] of symmetric groups S n {S_n} and [ β ] [\beta ] of S m {S_m} were evaluated on a CDC 6400. Tables were obtained for 2 ⩽ n ⩽ 10 2 \leqslant n \leqslant 10 and 2 ⩽ m ⩽ 5 2 \leqslant m \leqslant 5 as well as for m = 6 m = 6 and 2 ⩽ n ⩽ 7 2 \leqslant n \leqslant 7 .