If $W$ is a finite Coxeter group then the associated **Solomon’s descent algebra** is certain subalgebra $\Sigma[W]$ of the integral group algebra $\mathbf{Z}[W]$ discovered/introduced in

- L. Solomon,
*A Mackey formula in the group ring of a Coxeter group*, J. Algebra**41**, (1976), 255-268, MR0444756, doi

Other literature

- Mike Atkinson,
*A new proof of a theorem of Solomon*, Bull. London Math. Soc.**18**(1986), 351-354;*Solomon’s descent algebra revisited*, Bull. London Math. Soc. 24 (1992), 545-551. - Goetz Pfeiffer,
*A quiver presentation for Solomon’s descent algebra*, arxiv/0709.3914 - Israel Gelfand, D. Krob, Alain Lascoux, B. Leclerc, V. S. Retakh, J.-Y. Thibon,
*Noncommutative symmetric functions*, hep-th/9407124

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