Bonnafé, Cédric A note on the Grothendieck ring of the symmetric group. (English) Zbl 1102.20009 C. R., Math., Acad. Sci. Paris 342, No. 8, 533-538 (2006). Summary: Let \(p\) be a prime number and let \(n\) be a non-zero natural number. We compute the descending Loewy series of the algebra \({\mathcal R}_n/p{\mathcal R}_n\), where \({\mathcal R}_n\) denotes the ring of virtual ordinary characters of the symmetric group \(\mathcal S_n\). Cited in 1 ReviewCited in 1 Document MSC: 20C30 Representations of finite symmetric groups 19A22 Frobenius induction, Burnside and representation rings 05E10 Combinatorial aspects of representation theory Keywords:Young subgroups; symmetric groups; permutation modules; rings of virtual characters; Loewy filtrations; Grothendieck rings PDFBibTeX XMLCite \textit{C. Bonnafé}, C. R., Math., Acad. Sci. Paris 342, No. 8, 533--538 (2006; Zbl 1102.20009) Full Text: DOI arXiv References: [1] Curtis, C. W.; Reiner, I., Methods of Representation Theory, vol. I, With Applications to Finite Groups and Orders, Wiley Classics Library (1990), A Wiley-Interscience Publication, John Wiley & Sons, Inc.: A Wiley-Interscience Publication, John Wiley & Sons, Inc. New York, (Reprint of the 1981 original) [2] Geck, M.; Pfeiffer, G., Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras, London Math. Soc. Monogr. (N.S.), vol. 21 (2000), The Clarendon Press, Oxford University Press: The Clarendon Press, Oxford University Press New York · Zbl 0996.20004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.