Séminaire Lotharingien de Combinatoire, 89B.54 (2023), 12 pp.

Young-Hun Kim and Semin Yoo

Modules of the 0-Hecke Algebras for Genomic Schur Functions

Abstract. We construct an H_m(0)-module G_λ;m whose image under the quasisymmetric characteristic is the mth degree homogeneous component of the genomic Schur function U_λ by defining an H_m(0)-action on increasing gapless tableaux. We then provide a direct sum decomposition of G_λ;m and show that each summand of this decomposition is isomorphic to a weak Bruhat interval module.

Received: November 15, 2022. Accepted: February 20, 2023. Final version: April 1, 2023.

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