5 papers · 1 filter
Representations of finite matrix monoids
Nate Harman, Andrew Snowden, Elad Zelingher
Let be the multiplicative monoid of matrices over a finite field. The monoid algebra has been studied for several decades…
Kronecker Coefficients, Crystals, and Bitableaux
Nate Harman, Alexander N. Wilson
What might a combinatorial interpretation of the Kronecker coefficients even look like? We introduce a class of combinatorial objects called bitableaux, which we believe are a natu…
Classical interpolation categories
Nate Harman, Andrew Snowden
We study tensor categories that interpolate the representation categories of finite classical groups. There are (at least) two ways to approach these categories: via ultraproducts…
Tensor spaces and the geometry of polynomial representations
Nate Harman, Andrew Snowden
A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneo…
Higher Congruences in Character Tables
Nate Harman, Joshua Mundinger
Motivated by recent work of Peluse and Soundararajan on divisibility properties of the entries of the character tables of symmetric groups, we investigate the question: For a finit…