Modular representation theory of BIB designs

Constructions of nested directed BIB designs

A directed BIB design DB(k, A; v) is a BIB design B(k, 2A; v) in which the blocks are transitively ordered k-tuples and each ordered pair of elements occurs in exactly A blocks. A nested directed BIB design NDB(k, A; v) of form IT2<n<k-l(njn, An)in is a DB(k, A; v) where each block contains E2<n<k-l injn mutually disjoint subblocks, injn subblocks of which are partitIoned into in mutually disjo...

Ghosts in Modular Representation Theory

A ghost over a finite p-group G is a map between modular representations of G which is invisible in Tate cohomology. Motivated by the failure of the generating hypothesis—the statement that ghosts between finite-dimensional G-representations factor through a projective—we define the ghost number of kG to be the smallest integer l such that the composite of any l ghosts between finite-dimensiona...

A Brief Summary of Modular Representation Theory

This paper shall provide a brief summary of representation theory, with a focus on how the semi-simple case differs from the modular case. It will be assumed that the reader has a reasonable background in algebra, but not assuming an existing understand of representation theory.

Notes on the structure of support in BIB designs

Modular Representation Theory and the CDE Triangle