The Alperin and Dade conjectures for the Conway simple group \(Co_1\).
The authors continue their mission to verify the Alperin and Dade conjectures for all the sporadic simple groups. These deep conjectures relate the numbers of ordinary irreducible characters of given defect in a finite group to corresponding numbers in certain local subgroups, via an alternating sum formula. The verification comes in two parts: first a detailed analysis of the maximal local subgroups reveals which local subgroups need to be studied, and then their character tables are computed, so that the numbers of characters with the required properties can be read off. In this paper the local analysis is presented in full, and the character calculations are very sensibly suppressed -- a webpage with more details is provided for those who are interested.
scientific article; zbMATH DE number 2093329