Modules of the 0-Hecke algebra arising from standard permuted composition tableaux

Permuted Composition Tableaux, 0-hecke Algebra and Labeled Binary Trees

We introduce a generalization of semistandard composition tableaux called permuted composition tableaux. These tableaux are intimately related to permuted basement semistandard augmented fillings studied by Haglund, Mason and Remmel. Our primary motivation for studying permuted composition tableaux is to enumerate all possible ordered pairs of permutations (σ1, σ2) that can be obtained by stand...

Quasisymmetric Schur functions and modules of the 0-Hecke algebra

We define a 0-Hecke action on composition tableaux, and then use it to derive 0-Hecke modules whose quasisymmetric characteristic is a quasisymmetric Schur function. We then relate the modules to the weak Bruhat order and use them to derive a new basis for quasisymmetric functions. We also classify those modules that are tableau-cyclic and likewise indecomposable. Finally, we develop a restrict...

A Subalgebra of 0-hecke Algebra

Let (W, I) be a finite Coxeter group. In the case where W is a Weyl group, Berenstein and Kazhdan in [BK] constructed a monoid structure on the set of all subsets of I using unipotent χ-linear bicrystals. In this paper, we will generalize this result to all types of finite Coxeter groups (including non-crystallographic types). Our approach is more elementary, based on some combinatorics of Coxe...

Affine Hecke algebras and generalized standard Young tableaux

This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite-dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the weight space structure of finite-dimensional modules for the affine Hecke algebra. Using these indexing sets we show that (1) irreducible calibrated representa...

Vertex Operator Algebra Structure of Standard Affine Lie Algebra Modules