On the relationship between combinatorial functions and representation theory

DOI10.1007/s10688-017-0165-4zbMath1369.20013arXiv1612.09088OpenAlexW2595830273MaRDI QIDQ2364479

Natalia V. Tsilevich, Anatoly M. Vershik

Publication date: 21 July 2017

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.09088

zbMATH Keywords

skew-symmetric matricesinversion numbermajor indexdescent numberrepresentations of the symmetric groupdual complexity

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30)

Related Items (2)

On the dual complexity and spectra of some combinatorial functions ⋮ A natural idempotent in the descent algebra of a finite Coxeter group

Cites Work

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• The serpentine representation of the infinite symmetric group and the basic representation of the affine Lie algebra \(\widehat{\mathfrak{sl}_2}\).
• Eulerian quasisymmetric functions
• A decomposition of Solomon's descent algebra
• Permutation statistics and partitions
• Binomial posets, Möbius inversion, and permutation enumeration
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• Counting permutations with given cycle structure and descent set
• Major Index and Inversion Number of Permutations
• Representations of the Symmetric Group in Deformations of the Free Lie Algebra
• On the Netto Inversion Number of a Sequence
• q-Bernoulli and Eulerian Numbers

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