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Permutahedra, Lusztig varieties, degenerations, and subdivisions
Allen Knutson, Mario Sanchez, Melissa Sherman-Bennett
We present an embedded (in ) degeneration of Lusztig varieties (which generalize type Hessenberg varieties) to certain unions of Richardson varieties, giving a simultaneou…
Unexpected toric Richardson varieties
Eugene Gorsky, Soyeon Kim, Melissa Sherman-Bennett
We prove that an open Richardson variety in the complete flag variety for is isomorphic to a torus if and only if the corresponding closed Richardson variety is tor…
Braid variety cluster structures, II: general type
Pavel Galashin, Thomas Lam, Melissa Sherman-Bennett
We show that braid varieties for any complex simple algebraic group are cluster varieties. This includes open Richardson varieties inside the flag variety .
Comparing cluster algebras on braid varieties
Roger Casals, Pavel Galashin, Mikhail Gorsky +3
Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, posi…