A natural idempotent in the descent algebra of a finite Coxeter group

DOI10.5802/alco.310OpenAlexW4388555029MaRDI QIDQ6200572

Paul Renteln

Publication date: 1 March 2024

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/alco.310

zbMATH Keywords

idempotentsCoxeter groupcentral limit theoremsdescentspermutation representationdescent algebrareflection representation

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Representations of finite symmetric groups (20C30) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Combinatorial aspects of groups and algebras (05E16)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Diagonalization of matrices of statistics
• The distance spectra of Cayley graphs of Coxeter groups
• A decomposition of the descent algebra of a finite Coxeter group
• A decomposition of Solomon's descent algebra
• On the quiver of the descent algebra.
• Permutation statistics and partitions
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• A proof of Solomon's rule
• Semigroups, rings, and Markov chains
• On the dual complexity and spectra of some combinatorial functions
• A central limit theorem for a new statistic on permutations
• A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements
• A central limit theorem for the two-sided descent statistic on Coxeter groups
• On the central limit theorem for the two-sided descent statistics in Coxeter groups
• Asymptotics of a locally dependent statistic on finite reflection groups
• On the relationship between combinatorial functions and representation theory
• Spectral properties of descent algebra elements.
• Combinatorics of Permutations
• Spectra of Symmetrized Shuffling Operators
• Combinatorics of Coxeter Groups
• Finite Reflection Groups
• Solomon's Descent Algebra Revisited
• A New Proof of a Theorem of Solomon
• Major Index and Inversion Number of Permutations
• The Tutte polynomial of symmetric hyperplane arrangements
• Counting inversions and descents of random elements in finite Coxeter groups
• Eulerian Numbers
• On the Netto Inversion Number of a Sequence
• q-Bernoulli and Eulerian Numbers
• The flag major index and group actions on polynomial rings.
• Reflection groups and invariant theory

This page was built for publication: A natural idempotent in the descent algebra of a finite Coxeter group