5 papers
Bruhat intervals that are large hypercubes
Jordan Ellenberg, Nicolas Libedinsky, David Plaza +2
We study the question of finding big Bruhat intervals that are poset hypercubes in the symmetric group . Using permutations suggested by AlphaEvolve (an evolutionary coding ag…
A remarkable functor on -modules
Joe Baine, Tasman Fell, Anna Romanov +2
We introduce a new functor on categories of modular representations of reductive algebraic groups. Our functor has remarkable properties. For example it is a tensor functor and sen…
Equivariant neural networks and piecewise linear representation theory
Joel Gibson, Daniel Tubbenhauer, Geordie Williamson
Equivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simpl…
4-Strand Burau is Unfaithful Modulo 5
Joel Gibson, Geordie Williamson, Oded Yacobi
We introduce a new algorithm for finding kernel elements in the Burau representation. Our algorithm applies reservoir sampling to a statistic on matrices which is closely correlate…
Calculating the -canonical basis of Hecke algebras
Joel Gibson, Lars Thorge Jensen, Geordie Williamson
We describe an algorithm for computing the -canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category direc…