THE PROJECTIVE COVER OF TABLEAU-CYCLIC INDECOMPOSABLE Hn(0)-MODULES

초록

Let alpha be a composition of n and sigma a permutation in (sic)(l(alpha)). This paper concerns the projective covers of H-n(0)-modules V-alpha, X-alpha, and S-alpha(sigma) whose images under the quasisymmetric characteristic are the dual immaculate quasisymmetric function, the extended Schur function, and the quasisymmetric Schur function when sigma is the identity, respectively. First, we show that the projective cover of V-alpha is the projective indecomposable module P alpha due to Norton, and X-alpha and the-twist of the canonical submodule S-beta ,C(sigma) of S-beta(sigma) for (Q, sigma)'s satisfying suitable conditions appear as homomorphic images of V alpha. Second, we introduce a combinatorial model for the-twist of S-alpha(sigma) and derive a series of surjections starting from P-alpha to the-twist of S-alpha,C(i)d. Finally, we construct the projective cover of every indecomposable direct summand S-alpha,E(sigma) of S-alpha(sigma). As a byproduct, we give a characterization of triples (sigma, alpha, E) such that the projective cover of S-alpha,E(sigma) is indecomposable.

키워드