3 problems

Last-row Schur module conjecture. The last nonzero syzygy space is

Schur functor Chern character polynomiality conjecture. Each $G_i(E,\lambda)$ has degree $i$ both as an element of the Chow ring of $X$ and as a polynomial in $\lambda$. In particu…

Let $T(V)$ be the tensor algebra of a vector space $V$, and let $B_k(T(V))$ be its $k$th lower central series quotient. For a Young diagram $\lambda$, let $\mathcal{G}_\lambda$ den…