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2017 Combinatorial curve neighborhoods for the affine flag manifold of type $A_1^1$
Leonardo C. Mihalcea, Trevor Norton
Involve 10(2): 317-325 (2017). DOI: 10.2140/involve.2017.10.317


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 = ( d 0 , d 1 ) 0 2 , 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 A 1 1 .


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Leonardo C. Mihalcea. Trevor Norton. "Combinatorial curve neighborhoods for the affine flag manifold of type $A_1^1$." Involve 10 (2) 317 - 325, 2017.


Received: 13 December 2015; Accepted: 1 April 2016; Published: 2017
First available in Project Euclid: 13 December 2017

zbMATH: 1350.05180
MathSciNet: MR3574303
Digital Object Identifier: 10.2140/involve.2017.10.317

Primary: 05E15
Secondary: 14M15 , 17B67

Keywords: affine flag manifolds , curve neighborhood , moment graph

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.10 • No. 2 • 2017
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