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- Qëndrim R. Gashi
- 2009

Fix a Dynkin graph and let λ be a coweight. When does there exist an element w of the corresponding Weyl group such that w is λ-minuscule and w(λ) is dominant? We answer this question for general Coxeter groups. We express and prove these results using a variant of Mozes’s game of numbers.

- Qëndrim R. Gashi, Travis Schedler, David E. Speyer
- J. Comb. Theory, Ser. A
- 2012

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 boundary of the Tits cone. We give a simple proof that all configurations in the orbit are obtainable from each other by playing the numbers game, and give a strategy for going… (More)

- Qëndrim R. Gashi
- 2009

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 to the non-emptiness of certain affine Deligne-Lusztig varieties.

- Qëndrim R. Gashi
- 2007

Consider a root system R and the corresponding toric variety VR whose fan is the Weyl fan and whose lattice of characters is given by the root lattice for R. We prove the vanishing of the higher cohomology groups for certain line bundles on VR by proving a purely combinatorial result for root systems. These results are related to a converse to Mazur’s… (More)

Toric varieties associated with root systems appeared very naturally in the theory of group compactifications. Here they are considered in a very different context. We prove the vanishing of higher cohomology groups for certain line bundles on toric varieties associated to GLn and G2. This can be considered of general interest and it improves the previously… (More)

Toric varieties associated with root systems appeared very naturally in the theory of group compactifications. Here they are considered in a very different context. We prove the vanishing of higher cohomology groups for certain line bundles on toric varieties associated to GLn and G2. This can be considered of general interest and it improves the previously… (More)

- Qëndrim R. Gashi
- 2013

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, and special means that the bundle is torus-equivariant such that the character of the line bundle that corresponds to a maximal Weyl chamber is dominant with respect to that… (More)

Vanishing of higher cohomology groups for certain line bundles on some toric varieties arising from GLn is proved. A weaker statement is proved for G2. These two results imply a converse to Mazur’s Inequality for GLn and G2 respectively. Dedicated to Scarlett MccGwire and Christian Duhamel

- Qëndrim R. Gashi
- 2007

We prove a result involving root systems that implies a converse to Mazur’s inequality for all split groups, conjectured by Kottwitz and Rapoport (see e.g. [6]). This was previously known for classical groups (see e.g. [7]) and G2 (see e.g. [3]).

- Qëndrim R. Gashi
- 2008

We prove a result involving root systems that implies a converse to Mazur’s inequality for all split groups, conjectured by Kottwitz and Rapoport (see [10]). This was previously known for classical groups (see [11]) and G2 (see [5]).

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