Abstract

D. Benson used the notion of a spin regular partition to describe all irreducible modules of alternating groups over a field of characteristic 2. To determine which of these modules are self-dual, we use a bijection, due to M. Bressoud, between the strict odd partitions and the spin regular partitions of an integer n.

Now a 2-modular irreducible module of a finite group has quadratic type if its projective cover affords a quadratic geometry. In recent joint work with R. Gow, we showed that the number of quadratic type irreducible modules equals the number of strongly real 2-regular classes.

Euler’s partition theorem is that the number of odd partitions of n equals the number of strict partitions of n. Quite different bijective proofs were discovered by Sylvester and Glaisher. In order to determine the quadratic type of the irreducible modules of the double covers of alternating groups we need a new correspondence between the odd and strict partitions which combines properties of the classical bijections.

Euler’s partition theorem is that the number of odd partitions of n equals the number of strict partitions of n. Quite different bijective proofs were discovered by Sylvester and Glaisher. In order to determine the quadratic type of the irreducible modules of the double covers of alternating groups we need a new correspondence between the odd and strict partitions which combines properties of the classical bijections.