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

Abstract:

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