2 citations · 5 across the 7 of their papers we have counts for
7 papers
A Bollobás-type problem: from root systems to Erdős-Ko-Rado
Patrick J. Browne, Qëndrim R. Gashi, Padraig Ó Catháin
Motivated by an Erdős--Ko--Rado type problem on sets of strongly orthogonal roots in the root system, we estimate bounds for the size of a family of pairs $(A_{i}, B_{i}…
Normality and quadraticity for special ample line bundles on toric varieties arising from root systems
Qëndrim R. Gashi, Travis Schedler
We prove that special ample line bundles on toric varieties arising from root systems are projectively normal. Here the maximal cones of the fans correspond to the Weyl chambers, a…
Looping of the numbers game and the alcoved hypercube
Qëndrim R. Gashi, Travis Schedler, David E. Speyer
We study in detail the so-called looping case of Mozes's game of numbers, which concerns the (finite) orbits in the reflection representation of affine Weyl groups situated on the…
On dominance and minuscule Weyl group elements
Qëndrim R. Gashi, Travis Schedler
Fix a Dynkin diagram and let p be a coweight. When does there exist an element w of the corresponding Weyl group such that w is p-minuscule and w(p) is dominant? We answer this que…
On a conjecture of Kottwitz and Rapoport
Qëndrim R. Gashi
We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur's Inequality for all split and quasi-split (connected) reductive groups. These results are related…
A Vanishing Result for Toric Varieties Associated with Root Systems
Qëndrim R. Gashi
Consider a root system and the corresponding toric variety whose fan is the Weyl fan and whose lattice of characters is given by the root lattice for . We prove the va…