PERCENTAGE-AVOIDING, NORTHWEST SHAPES AND PEELABLE TABLEAUX

We prove three results for Specht and Schur modules associated to nort hwest and the more general class of %-avoiding shapes. The first resul t (conjectured for northwest shapes in by the authors) is a generaliza tion the Littlewood-Richardson rule, giving an explicit combinatorial description for the multiplicities of irreducibles in the Specht and S chur modules of a %-avoiding shape D, in terms of D-peelable tableaux. The second result gives three involutions on the set of peelable tabl eaux which exhibit the symmetries of these multiplicities correspondin g to three natural involutive operations on the set of %-avoiding shap es. The third result gives branching rules for the Specht and Schur mo dules of northwest shapes. The proofs are all combinatorial, with the exception of a key step in the first result, which requires results of Magyar on configuration varieties and characters of flagged Schur mod ules. (C) 1998 Academic Press.