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The Cartan matrix of the Schur algebra S(2, r)
Authors:A E Henke
Institution:Universit?t Gesamthochschule Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany, DE
Abstract: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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