An inversion formula for the primitive idempotents of the trivial source algebra |
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| Affiliation: | 1. Institut de recherche en mathématique et physique, Université catholique de Louvain, Chemin du Cyclotron 2, B 1348 Louvain-la-Neuve, Belgique;2. Dipartimento di matematica, Università degli studi di Milano, Via C. Saldini 50, 20133 Milano, Italy;3. Dipartimento di matematica e informatica, Università degli studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy;4. Department of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario, K1N 6N5, Canada;1. Department of Mathematics, Stanford University, Stanford, CA 94305, United States of America;2. Department of Mathematics and Statistics, SUNY, Albany, NY 12222, United States of America;1. Department of Mathematics and Statistics, University of South Alabama, United States of America;2. Department of Mathematics, Wingate University, United States of America;1. Department of Mathematics, Washington University, Saint Louis, MO 63130, USA |
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| Abstract: | ![]()
Formulas for the primitive idempotents of the trivial source algebra, in characteristic zero, have been given by Boltje and Bouc–Thévenaz. We shall give another formula for those idempotents, expressing them as linear combinations of the elements of a canonical basis for the integral ring. The formula is an inversion formula analogous to the Gluck–Yoshida formula for the primitive idempotents of the Burnside algebra. It involves all the irreducible characters of all the normalizers of p-subgroups. As a corollary, we shall show that the linearization map from the monomial Burnside ring has a matrix whose entries can be expressed in terms of the above Brauer characters and some reduced Euler characteristics of posets. |
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| Keywords: | Trivial source ring Table of marks Monimial Burnside ring |
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