The peak algebra and the Hecke-Clifford algebras at $q=0$

Diagram supermodules for $0$-Hecke-Clifford algebras

We introduce a general method for constructing modules for $0$-Hecke algebras and supermodules for $0$-Hecke-Clifford algebras from diagrams of boxes in the plane, and give formulas for the images of these modules in the algebras of quasisymmetric functions and peak functions under the relevant characteristic map. As initial applications, we resolve a question of Jing and Li (2015), introduce a new basis of the peak algebra analogous to the quasisymmetric Schur functions, uncover a new connection between Schur $Q$-functions and quasisymmetric Schur functions, give a representation-theoretic in…

Hecke-Clifford 超代数在根之 unity 时的表示

Representations of Hecke-Clifford superalgebras at roots of unity

本文研究了有理 Hecke-Clifford 超代数在 q² 为 h 阶单位根时的不可约完全可分表示分类，并推导了有限 Hecke-Clifford 超代数 semisimple 的充要条件。

Representation theory of 0-Hecke-Clifford algebras

The representation theory of 0-Hecke-Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron et al. have proved that the Grothendieck ring of the category of finitely generated supermodules of 0-Hecke-Clifford algebras is isomorphic to the algebra of peak quasisymmetric functions defined by Stembridge. In this paper we further study the category of finitely generated projective supermodules and clarify the correspondence between it and the peak algebra of symmetric groups. In particular, two kinds of restriction rules for induced projective s…

Murnaghan-Nakayama规则与Hecke-Clifford代数的自旋双迹

Murnaghan-Nakayama rule and spin bitrace for the Hecke-Clifford Algebra

本文为Hecke-Clifford代数导出Pfaffian型Murnaghan-Nakayama规则，基于Frobenius公式和顶点算子，进而得到不可约特征标的一般公式、迭代公式、特殊划分的紧凑公式、对称性质及自旋双迹的组合公式，并列出n≤7的特征标表。

0-Hecke 模、多米诺骨牌表与 B 型拟对称函数

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

本文将升序相容推广至所有 Coxeter 群以构造 0-Hecke 模，并在 B 型中解释拟对称、峰函数及移位多米诺函数，证明正展开与限制特征公式。

Hopf对偶对的偏斜Murnaghan–Nakayama规则

A skew Murnaghan--Nakayama rule for Hopf dual pairs

基于Hopf对偶对的偏斜Murnaghan–Nakayama规则，通过完全Cauchy元素和部分收缩算子建立统一理论，推广经典规则并得到新公式，应用于Ariki–Koike代数特征标和偏斜Kostka多项式，验证了Walker猜想。