Meeting Details

Title: "Specht Modules and the Plucker Algebra" Ph.D. Oral Comprehensive Examination Nick Early, Adviser: Sergei Tabachnikov, Penn State http:// We summarize on-going work with L. Oeding on certain subalgebras $\mathcal{M}_{2}$ of the Plucker algebra, that are generated by compound determinants, in the special case where the Plucker variables are $3 \times 3$ minors of a $3\times 6$ matrix. It is known that two of these generators appear as "special" variables in the cluster algebra of the Grassmannian Gr$_3(6)$. The problem of classifying these special cluster variables for Gr$_k(n)$ for arbitrary $k$ and $n$ remains open. I show how these variables give a new basis for the Specht module associated to the $3\times 2$ Young tabloid. With L. Oeding, we conjecture a presentation for the algebra $\mathcal{M}_2$.