Work

Atomic length on Weyl groups

Year: 2024

Type: article

Abstract: We define a new statistic on Weyl groups called the atomic length and investigate its combinatorial and representation-theoretic properties. In finite types, we show a number of properties of the atomic length which are reminiscent of the properties of the usual length. Moreover, we prove that, with the exception of rank two, this statistic describes an interval. In affine types, our results shed some light on classical enumeration problems, such as the celebrated Granville–Ono theorem on the existence of core partitions, by relating the atomic length to the theory of crystals.

Source: Journal of Combinatorial Algebra

DOI: 10.4171/jca/104

Authors: Nathan Chapelier-Laget, Thomas Gerber

Institutions: The University of Sydney, Université du littoral côte d'opale, Lyon 1 Université

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Agence Nationale de la Recherche, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Awards: Combinatorial representation theory and interactions with probabilistic models, Representations of finite groups and quantum groups: categorification, combinatorics and interactions