We study (G, 2)-arc-transitive graphs for innately transitive permutation groups G such that G can be embedded into a wreath product SymΓwr Sl acting in product action on Γ. We find two such connected graphs: the first is Sylvester’s double six graph with 36 vertices, while the second is a graph with 120 vertices whose automorphism group is Aut Sp(4, 4). We prove that under certain conditions n...

It is shown that statistics on the wreath product groups, Ck �Sn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck � Sn. Finally, some new statistics on Ck � Sn are introduced, inspired by lecture hall theory, and their distributions are derived.

Let W be a complex reflection group. We formulate a conjecture relating blocks of the corresponding restricted rational Cherednik algebras and Rouquier families for cyclotomic Hecke algebras. We verify the conjecture in the case that W is a wreath product of a symmetric group with a cyclic group of order l.

It is shown that statistics on the wreath product groups, Ck oSn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck oSn. Finally, some new statistics on Ck oSn are introduced, inspired by lecture hall theory, and their distributions are derived.

We describe a generalization of Hashimoto and Kurano's Cauchy filtration for divided powers algebras. This is then used to provide cellular structure generalized Schur algebras associated an arbitrary algebra. Applications the cellularity wreath product A ? S d are also considered.