Séminaire Lotharingien de Combinatoire, 85B.69 (2021), 12 pp.
Seung-Il Choi, Young-Hun Kim, Sun-Young Nam and Young-Tak Oh
Modules of the 0-Hecke Algebra Arising from Standard Permuted Composition Tableaux
Abstract.
We study structures of the Hn(0)-module Sσα arising from standard permuted composition tableaux of shape α and type σ.
Precisely,
we investigate the indecomposability of Sσα, the characteristic relations among Sσα's, the quasisymmetric Schur-expansion of the image of Sσα under the quasisymmetric characteristic, and the projective cover of every indecomposable direct summand
Sσα,E
of Sσα.
And then, we reveal hidden connections to other indecomposable Hn(0)-modules Vα and Xα arising from standard immaculate tableaux and standard extended tableaux, respectively.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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