Generalized blocks for symmetric groups

On defect groups for generalized blocks of the symmetric group

In a paper of 2003, B. Külshammer, J. B. Olsson and G. R. Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal l-block. We then check that, in the Abelian case, we have an analogue of one of M. Broué’s conjectures.

On generalized blocks for alternating groups

In a recent paper Külshammer, Olsson, Robinson gave a danalogue for the Nakayama conjecture for symmetric groups where d ≥ 2 is an arbitrary integer. We prove that there is a natural d-analogue of the Nakayama conjecture for alternating groups whenever d is 2 or an arbitrary odd integer greater than 1. This generalizes an old result of Kerber.

Projective Representations of Generalized Symmetric Groups

Representations of the Generalized Symmetric Groups

Generalized Symmetric Berwald Spaces

In this paper we study generalized symmetric Berwald spaces. We show that if a Berwald space $(M,F)$ admits a parallel $s-$structure then it is locally symmetric. For a complete Berwald space which admits a parallel s-structure we show that if the flag curvature of $(M,F)$ is everywhere nonzero, then $F$ is Riemannian.