Involve: A Journal of Mathematics

  • Involve
  • Volume 10, Number 2 (2017), 317-325.

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

Leonardo C. Mihalcea and Trevor Norton

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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 .

Article information

Involve, Volume 10, Number 2 (2017), 317-325.

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

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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]

affine flag manifolds moment graph curve neighborhood


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.

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