Involve: A Journal of Mathematics
- Volume 10, Number 2 (2017), 317-325.
Combinatorial curve neighborhoods for the affine flag manifold of type $A_1^1$
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 .
Involve, Volume 10, Number 2 (2017), 317-325.
Received: 13 December 2015
Accepted: 1 April 2016
First available in Project Euclid: 13 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]
Secondary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
Mihalcea, Leonardo C.; Norton, Trevor. Combinatorial curve neighborhoods for the affine flag manifold of type $A_1^1$. Involve 10 (2017), no. 2, 317--325. doi:10.2140/involve.2017.10.317. https://projecteuclid.org/euclid.involve/1513135633