Séminaire Lotharingien de Combinatoire, 89B.53 (2023), 12 pp.
Colin Defant and Dominic Searles
I>Hecke Modules, Quasisymmetric Functions, and Peak Functions in Type B
Abstract.
We extend the recently-introduced ascent-compatibility framework to arbitrary Coxeter systems, yielding a uniform method for constructing modules of 0-Hecke algebras. In type B, we apply this method to produce 0-Hecke modules whose type B quasisymmetric characteristics are notable type B quasisymmetric functions. We also construct a 0-Hecke module on the set of standard domino tableaux of a given shape; the type B quasisymmetric characteristic of this module is a certain type B analogue of a Schur function called a domino function. We then introduce an analogous function defined on shifted domino tableaux and prove that this function expands positively in the type B analogue of the peak functions. Finally, we introduce a type B variant of the 0-Hecke-Clifford algebra and consider the modules of this algebra induced from the simple type B 0-Hecke modules. We characterize the isomorphism classes of these induced modules in terms of type B peak sets and prove that the type B quasisymmetric characteristics of the restrictions of these induced modules are precisely the type B peak functions.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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