Identities in representation theory via chain complexes (Q1330039)

In the last few years alternating sums appeared surprisingly often in connection with the representation theory of finite groups. For example Knörr and Robinson showed that Alperin's weight conjecture is equivalent to an equation involving an alternating sum. A more general conjecture about the value of another alternating sum was stated recently by Dade. This paper can be regarded as an example where it is possible to interpret certain alternating sums arising from the canonical Brauer induction formula as Euler characteristics of chain complexes and to transform these by finding homotopy equivalent chain complexes. The chain complexes we construct arise from coefficient systems on the simplicial complexes of certain posets.