nLab descent algebra

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