Cuspidal modules of finite general linear group

Rook theory of the finite general linear group

Matrices over a finite field having fixed rank and restricted support are a natural qanalogue of rook placements on a board. We develop this q-rook theory by defining a corresponding analogue of the hit numbers. Using tools from coding theory, we show that these q-hit and q-rook numbers obey a variety of identities analogous to the classical case. We also explore connections to earlier q-analog...

Inequalities for Finite Group Permutation Modules

If f is a nonzero complex-valued function defined on a finite abelian group A and f̂ is its Fourier transform, then | supp(f)|| supp(f̂)| ≥ |A|, where supp(f) and supp(f̂) are the supports of f and f̂ . In this paper we generalize this known result in several directions. In particular, we prove an analogous inequality where the abelian group A is replaced by a transitive right G-set, where G is an ...

Generic Idempotent Modules for a Finite Group

Let G be a nite group and k an algebraically closed eld of characteristic p. Let F U be the Rickard idempotent kG-module corresponding to the set U of subvarieties of the cohomology variety VG which are not irreducible components. We show that F U is a nite sum of generic modules corresponding to the irreducible components of VG. In this context, a generic module is an indecomposable module of ...

On the U−module Structure of Unipotent Specht Modules of Finite General Linear Groups

Hook Modules for General Linear Groups

For an arbitrary infinite field k of characteristic p > 0, we completely describe the structure of a block of the algebraic monoid Mn(k) (all n×n matrices over k), or, equivalently, a block of the Schur algebra S(n, p), whose simple modules are indexed by p-hook partitions. This leads to a character formula for certain simple GLn(k)-modules, valid for all n and all p.