79 citations · 635 across the 51 of their papers we have counts for
4 papers · 1 filter
The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula
Pamela E. Harris, Erik Insko, Lauren Kelly Williams
Even though weight multiplicity formulas, such as Kostant's formula, exist their computational use is extremely cumbersome. In fact, even in cases when the multiplicity is well und…
Positively oriented matroids are realizable
Federico Ardila, Felipe Rincón, Lauren Williams
We prove da Silva's 1987 conjecture that any positively oriented matroid is a positroid; that is, it can be realized by a set of vectors in a real vector space. It follows from thi…
Positroids and non-crossing partitions
Federico Ardila, Felipe Rincón, Lauren Williams
We investigate the role that non-crossing partitions play in the study of positroids, a class of matroids introduced by Postnikov. We prove that every positroid can be constructed…
The full Kostant-Toda hierarchy on the positive flag variety
Yuji Kodama, Lauren Williams
We study some geometric and combinatorial aspects of the solution to the full Kostant-Toda (f-KT) hierarchy, when the initial data is given by an arbitrary point on the totally non…