Authors' names, email addresses and institutions:

Vladimir Shchigolev
Ulyanovsk State University


Short abstract:

Let $K$ be a field of characteristic $p>0$ and $\Sigma_n$
denote the symmetric group of degree $n$.
The formula for $Ext^1_{\Sigma_n}(D^\lambda,D^\mu)$,
where $p>2$, $D^\lambda$~is a completely splittable $K\Sigma_n$-module
and $\lambda$ does not strictly dominate~$\mu$, is obtained.
With its help, we calculate all composition multiplicities
of $D^\lambda\uparrow^{\Sigma_{n+1}}$, where
$D^\lambda$~is a completely splittable $K\Sigma_n$-module.
Similar formulae for extension, restriction and induction are
found for some other modules in the vicinity of
completely splittable modules.


Current status:

it is a preprint.