Let be the affine flag manifold of Lie type . Its moment graph encodes the torus fixed points (which are elements of the infinite dihedral group ) and the torus stable curves in . Given a fixed point and a degree , the combinatorial curve neighborhood is the set of maximal elements in the moment graph of which can be reached from using a chain of curves of total degree . In this paper we give a formula for these elements, using combinatorics of the affine root system of type .
"Combinatorial curve neighborhoods for the affine flag manifold of type $A_1^1$." Involve 10 (2) 317 - 325, 2017. https://doi.org/10.2140/involve.2017.10.317