Haralampos Geranios

activity

20162026

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Showing 2017Show all

7 papers · 1 filter

math.RT2017

First Degree Cohomology of Specht Modules and Extensions of Symmetric Powers

Stephen Donkin, Haralampos Geranios

Let $Σ_{d}$ denote the symmetric group of degree $d$ and let $K$ be a field of positive characteristic $p$ . For $p > 2$ we give an explicit description of the first cohomology group $H…

math.RT2017

Injective Schur Modules

Stephen Donkin, Haralampos Geranios

We determine the partitions $λ$ for which the corresponding induced module (or Schur module in the language of Buchsbaum et. al., [1]) $\nabla (λ)$ is injective in the category of p…

math.RT2017

Composition Factors of Tensor Products of Truncated Symmetric Powers

Stephen Donkin, Haralampos Geranios

Let $G$ be the general linear group of degree $n$ over an algebraically closed field $K$ of characteristic $p > 0$ . We study the $m$ -fold tensor product $S ˉ (E)^{\otimes m}$ of t…

math.RT2017

Invariants of Specht Modules

Stephen Donkin, Haralampos Geranios

In [14] Hemmer conjectures that the module of fixed points for the symmetric group $Σ_{m}$ of a Specht module for $Σ_{n}$ (with $n > m$ ), over a field of positive characteristic $p$ , has…

math.RT2017

Composition Factors of Tensor Products of Symmetric Powers

Stephen Donkin, Haralampos Geranios

We determine the composition factors of the tensor product $S (E) \otimes S (E)$ of two copies of the symmetric algebra of the natural module $E$ of a general linear group over an alg…

math.RT2017

Endomorphism Algebras of Some Modules for Schur Algebras and Representation Dimension

Stephen Donkin, Haralampos Geranios

We consider the representation dimension, for fixed $n \geq 2$ , of ordinary and quantised Schur algebras $S (n, r)$ over a field $k$ . For $k$ of positive characteristic $p$ we give a l…