Contents

Preface ix

Perverse coherent sheaves on the nilpotent cone in good characteristic

Pramod N. Achar 1

On the vanishing ranges for the cohomology of ﬁnite groups of Lie type II

Christopher P. Bendel, Daniel K. Nakano,

and Cornelius Pillen 25

Tilting modules for the current algebra of a simple Lie algebra

Matthew Bennett and Vyjayanthi Chari 75

Endotrivial modules

Jon F. Carlson 99

Super duality for general linear Lie superalgebras and applications

Shun-Jen Cheng, Ngau Lam, and Weiqiang Wang 113

Structures and representations of aﬃne q-Schur algebras

Jie Du 137

Multiplicative bases for the centres of the group algebra and Iwahori-Hecke

algebra of the symmetric group

Andrew Francis and Lenny Jones 159

Moonshine paths and a VOA existence proof of the Monster

Robert L. Griess Jr. 165

Characteristic polynomials and ﬁxed spaces of semisimple elements

Robert Guralnick and Gunter Malle 173

“Frobenius twists” in the representation theory of the symmetric group

David J. Hemmer 187

The generalized Kac-Wakimoto conjecture and support varieties for the Lie

superalgebra osp(m|2n)

Jonathan Kujawa 201

An approach towards the Koll´ ar-Peskine problem via the Instanton Moduli

Space

Shrawan Kumar 217

On the representations of disconnected reductive groups over Fq

G. Lusztig 227

vii