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arXiv · 2404.04961

0-Hecke Modules, Domino Tableaux, and Type-$B$ Quasisymmetric Functions

Colin Defant·Dominic Searles
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Abstract

We extend the notion of ascent-compatibility from symmetric groups to all Coxeter groups, thereby providing a type-independent framework for constructing families of modules of $0$-Hecke algebras. We apply this framework in type $B$ to give representation-theoretic interpretations of a number of noteworthy families of type-$B$ quasisymmetric functions. Next, we construct modules of the type-$B$ $0$-Hecke algebra corresponding to type-$B$ analogues of Schur functions and introduce a type-$B$ analogue of Schur $Q$-functions; we prove that these shifted domino functions expand positively in the type-$B$ peak functions. We define a type-$B$ analogue of the $0$-Hecke--Clifford algebra, and we use this to provide representation-theoretic interpretations for both the type-$B$ peak functions and the shifted domino functions. We consider the modules of this algebra induced from type-$B$ $0$-Hecke modules constructed via ascent-compatibility and prove a general formula, in terms of type-$B$ peak functions, for the type-$B$ quasisymmetric characteristics of the restrictions of these modules.

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BibTeXRIS

Colin Defant, Dominic Searles. 2024-04-07. 0-Hecke Modules, Domino Tableaux, and Type-$B$ Quasisymmetric Functions. https://arxiv.org/abs/2404.04961

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