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A natural idempotent in the descent algebra of a finite Coxeter group
Renteln, Paul1
1 California State University Department of Physics San Bernardino, CA 92407 USA
Algebraic Combinatorics, Volume 6 (2023) no. 5, pp. 1177-1188.

We construct a natural idempotent in the descent algebra of a finite Coxeter group. The proof is uniform (independent of the classification). This leads to a simple determination of the spectrum of a natural matrix related to descents. Other applications are discussed.

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DOI: 10.5802/alco.310
Classification: 05A05, 05C25, 05C50, 05E16
Keywords: Coxeter group, reflection representation, permutation representation, descents, descent algebra, idempotents, central limit theorems

Renteln, Paul 1

1 California State University Department of Physics San Bernardino, CA 92407 USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Renteln, Paul. A natural idempotent in the descent algebra of a finite Coxeter group. Algebraic Combinatorics, Volume 6 (2023) no. 5, pp. 1177-1188. doi : 10.5802/alco.310. https://alco.centre-mersenne.org/articles/10.5802/alco.310/

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