45 citations · 87 across the 6 of their papers we have counts for
7 papers
Quiver Bases of Cartan Squares of Minuscule Representations
David B Rush
We consider the Cartan square of a minuscule representation of a simply laced complex simple Lie algebra . We construct for a family of bases,…
Restriction of Global Bases and Rhoades's Theorem
David B Rush
It is shown that if is a multiple of a fundamental weight of , the lower global basis of the irreducible -representation with highe…
Computing the Lusztig--Vogan Bijection
David B Rush
Let be a connected complex reductive algebraic group with Lie algebra . The Lusztig--Vogan bijection relates two bases for the bounded derived category of -equ…
On Order Ideals of Minuscule Posets III: The CDE Property
David B Rush
Recent work of Hopkins establishes that the lattice of order ideals of a minuscule poset satisfies the coincidental down-degree expectations property of Reiner, Tenner, and Yong. H…
On Orbits of Order Ideals of Minuscule Posets II: Homomesy
David B. Rush, Kelvin Wang
The Fon-Der-Flaass action partitions the order ideals of a poset into disjoint orbits. For a product of two chains, Propp and Roby observed --- across orbits --- the mean cardinali…
Cyclic Sieving and Plethysm Coefficients
David B Rush
A combinatorial expression for the coefficient of the Schur function in the expansion of the plethysm is given for all dividing for the cases in…
On Orbits of Order Ideals of Minuscule Posets
David B Rush, XiaoLin Shi
An action on order ideals of posets considered by Fon-Der-Flaass is analyzed in the case of posets arising from minuscule representations of complex simple Lie algebras. For these…