A Combinatorial Formula for Orthogonal Idempotents in the $0$-Hecke Algebra of the Symmetric Group

Author:

Denton Tom

Abstract

Building on the work of P.N. Norton, we give combinatorial formulae for two maximal decompositions of the identity into orthogonal idempotents in the $0$-Hecke algebra of the symmetric group, $\mathbb{C}H_0(S_N)$. This construction is compatible with the branching from $S_{N-1}$ to $S_{N}$.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 9 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The projective cover of tableau-cyclic indecomposable _{}(0)-modules;Transactions of the American Mathematical Society;2022-09-02

2. Homological properties of 0-Hecke modules for dual immaculate quasisymmetric functions;Forum of Mathematics, Sigma;2022

3. Artin group injection in the Hecke algebra for right-angled groups;Geometriae Dedicata;2021-02-22

4. Simplicity of Augmentation Submodules for Transformation Monoids;Algebras and Representation Theory;2020-07-08

5. 2 ℜ $$\mathcal{R}$$ -trivial Monoids;Representation Theory of Finite Monoids;2016

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