4
votes
1answer
198 views

The Representation of $\mathrm{Sp}_{2n}$ of Dimension $2^n$ in characteristic 2

Let $G:=\mathrm{Sp}_{2n}$ be the simple algebraic group of simply connected type with root-system $C_n$. Is there a way, to explicitly construct the highest weight representation ...
1
vote
1answer
212 views

Sage or Magma Implementation of Nilpotent Orbit Varieties

For a given partition $[n_{1},...,n_{k}]$ of $N \in \mathbb{N}$ there exists a corresponding nilpotent orbit variety $O_{[n_{1},...,n_{k}]}$ in $\mathfrak{gl}(N)$ which can be represented by a set of ...
18
votes
7answers
1k views

Computer package for representation theory of the symmetric group

Is there a computer algebra package in which I can compute the following for representations of a specific symmetric group (e.g. $S_7$): (1) $V \otimes W$ (2) $S_\lambda V$, where $S_\lambda$ is a ...
7
votes
2answers
1k views

Compute Lie algebra cohomology

Is there a computer algebra system that is able to compute the Lie algebra cohomology in a given representation?what if the Lie algebra is finite dimensional? In my case I would like to be able to ...