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Séminaire Lotharingien de Combinatoire, 84B.37 (2020), 11 pp.

# Dominic Searles

# Extended Schur Functions and 0-Hecke Modules

**Abstract.**
Three bases of noncommutative symmetric functions have been described as Schur-like: the immaculate symmetric functions, the noncommutative Schur functions, and the shin functions. Each of these has a dual basis in quasisymmetric functions. Dual bases of the former two have been given a representation-theoretic interpretation in terms of 0-Hecke modules. We complete the picture by constructing 0-Hecke modules whose quasisymmetric characteristics are the extended Schur functions, the dual basis to the shin functions. These modules are indecomposable.

Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.

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