9 papers
Bounded Bruhat intervals and affine Coxeter groups
Grant T. Barkley, Christian Gaetz
Dyer (1991) proved that, for each fixed length , only finitely many isomorphism types of Bruhat intervals occur in finite Coxeter groups. In this short paper, we prove that this…
Totally nonnegative maximal tori and opposed Bruhat intervals
Grant T. Barkley, Steven N. Karp
Lusztig (2024) recently introduced the space of totally positive maximal tori of an algebraic group . Each such torus is the intersection of a totally positiv…
Combinatorial invariance for the coefficient of in Kazhdan-Lusztig polynomials
Grant T. Barkley, Christian Gaetz, Thomas Lam
We prove the combinatorial invariance of the coefficient of in Kazhdan--Lusztig polynomials for arbitrary Coxeter groups. As a result, we obtain the Combinatorial Invariance Co…
The BBDVW Conjecture for Kazhdan-Lusztig polynomials of lower intervals
Grant T. Barkley, Christian Gaetz
Blundell, Buesing, Davies, VeliÄkoviÄ, and Williamson (BBDVW) introduced the notion of a hypercube decomposition of an interval in Bruhat order. They conjectured a recursive form…
Affine extended weak order is a lattice
Grant T. Barkley, David E Speyer
Coxeter groups are equipped with a partial order known as the weak order, such that if the inversions of are a subset of the inversions of . In finite Coxeter gro…
On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials
Grant T. Barkley, Christian Gaetz
We show that the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic versi…