On D. E. Littlewood's Algebra of S-Functions

Abstract

Several papers have been written on the “new” multiplication of S-functions since Littlewood [3, p. 206] first suggested the problem. M. Zia-ud-Din [13] calculated the case {m} ⊗ {n} for mn ≤ 12, making use of the tables of the characters of the symmetric group of degree mn. Later Thrall [10,pp. 378-382] developed explicit formulae for the cases {m} ⊗ {2},{m} ⊗ {3}, {2} ⊗ {m} (where m is any integer).