Lawrence Rickard Wager—1904–1965

Some Examples of Rickard Complexes

After a presentation of Brou e's conjecture for principal blocks with an abelian defect group, we describe a Rickard complex for GL 2 (q) arising from thè-adic cohomology of a Deligne-Lusztig variety, in accordance with the explicit form given by Brou e to his conjecture in the case of Chevalley groups in non natural characteristic.

Rickard Equivalences and Block Theory

De nition We say that a subgroup H of G controls the fusion of p subgroups of G if the following two conditions are ful lled C H contains a Sylow p subgroup Sp of G C whenever P is a subgroup of Sp and g is an element of G such that gPg Sp there exist z in the centralizer CG P of P in G and h in H such that g hz Basic example We denote by Op G the largest normal subgroup of G with order prime t...

Block Theory via Stable and Rickard Equivalences

Lawrence Kruger

Higher Lawrence configurations

Any configuration of lattice vectors gives rise to a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. We prove finiteness results for the Markov bases, Graver bases and facet posets of these configurations, and we discuss applications to the statistical theory of log-linear models.