2018/09/28 by Laurence Barker, Barker, Laurence
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RT
paper · pdf · doi:10.48550/arxiv.1809.10984
arxiv created 2018/09/28 · arxiv updated 2018/10/01
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.