Vol. 10, No. 2, 2017

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Combinatorial curve neighborhoods for the affine flag manifold of type $A_1^1$

Leonardo C. Mihalcea and Trevor Norton

Vol. 10 (2017), No. 2, 317–325

Let X be the affine flag manifold of Lie type A11. Its moment graph encodes the torus fixed points (which are elements of the infinite dihedral group D) and the torus stable curves in X. Given a fixed point u D and a degree d = (d0,d1) 02, the combinatorial curve neighborhood is the set of maximal elements in the moment graph of X which can be reached from u using a chain of curves of total degree  d. In this paper we give a formula for these elements, using combinatorics of the affine root system of type A11.

affine flag manifolds, moment graph, curve neighborhood
Mathematical Subject Classification 2010
Primary: 05E15
Secondary: 17B67, 14M15
Received: 13 December 2015
Accepted: 1 April 2016
Published: 10 November 2016

Communicated by Jim Haglund
Leonardo C. Mihalcea
Department of Mathematics
Virginia Tech University
Blacksburg, VA 24061
United States
Trevor Norton
Department of Mathematics
Virginia Tech University
Blacksburg, VA 24061
United States