All Questions

Let $S_n$ be the symmetric group and $M_n$ the character table of $S_n$ as a matrix (in some order) for $n \geq 2$. Question: Is it true that the rank of $M_n$ as a matrix modulo $m$ for $m \geq 2$ ...

Suppose $V$ is a finite-dimensional vector space (over $\mathbb{C}$) and $\lambda$ is a partition of $n$ (not necessarily the dimension). Let $S^\lambda(V)=(V^{\otimes n})_\lambda$ be the $\lambda$'th ...

I am mainly looking for references on this subject, as I was unable to find any, at least any that answers what I am looking for to a satisfactory degree. As it is well-known and extremely easy to ...

I'm trying to understand the paper "Products and plethysms of characters with orthogonal, symplectic, and symmetric groups" by D.E. Littlewood (link), but I'm having trouble overcoming the language ...

I hope this is not too elementary for this site, but I already asked something similar on MSE which has not received any attention whatsoever. I am extremely unfamiliar with the algebraic/...

Let $V_n$ be the standard permutation representation of the symmetric group $S_n$, and let $\mathbb{S}_{\lambda}$ denote the Schur functor associated to the partition $\lambda$. Let $\lambda$ range ...