Abstract
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 analogs of Schur functions and introduce a type-B analog of Schur Q-functions; we prove that these shifted domino functions expand positively in the type-B peak functions. We define a type-B analog 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.
Published Version
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