Darstellungstheorietage and Nikolaus Conference 2013

Speaker: David Denoncin (Paris)

Title: About the Inductive AM Condition for the Simple Alternating Groups in Characteristic 2

Abstract: The Alperin-McKay conjecture goes back to 1972 when it was observed that for lots of finite groups \(G\) and a prime number \(p\), the number of characters of \(G\) whose degree is prime to \(p\) is the same as in the normalizer of a Sylow \(p\)-subgroup. The conjecture was later made more precise with the notion of \(p\)-blocks. Then Britta Späth reduced the problem to finite simple groups that should satisfy the "inductive AM condition", which involves their Schur cover.

I would first like to recall how irreducible complex characters are sorted out into blocks and the notion of height of a character to introduce the precise Alperin-McKay conjecture, then recall the inductive AM condition and discuss the method I used to verify the inductive AM condition for the alternating groups in characteristic 2 (which was the last characteristic that was not done yet for these groups).