A combinatorial model for the transition matrix between the Specht and -web bases

Abstract

We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases of the irreducible $ \mathfrak {S}_{2n} $ -representation indexed by $ (n,n) $ , which answers Rhoades’s question. Furthermore, we study enumerative properties of these permutations.