An inversion formula for the primitive idempotents of the trivial source algebra
Representation Theory
2018-10-01 v1
Abstract
Formulas for the primitive idempotents of the trivial source algebra, in characteristic zero, have been given by Boltje and Bouc--Th\'{e}venaz. 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 -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.
Keywords
Cite
@article{arxiv.1809.10984,
title = {An inversion formula for the primitive idempotents of the trivial source algebra},
author = {Laurence Barker},
journal= {arXiv preprint arXiv:1809.10984},
year = {2018}
}