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The Cartan matrix of the Schur algebra S(2, r)

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Let k be an infinite field of prime characteristic and let r be a positive integer. Using admissible decompositions, we determine explicitly the entries of the decomposition matrix of the Schur algebra S(2, r) over k and prove that any two blocks with the same number of simple modules have the same decomposition matrix and hence the same Cartan matrix.

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Received: 13.12.1999

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Henke, A. The Cartan matrix of the Schur algebra S(2, r). Arch. Math. 76, 416–425 (2001). https://doi.org/10.1007/PL00000452

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  • DOI: https://doi.org/10.1007/PL00000452

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