The Combinatorial Curve Neighborhoods of Affine Flag Manifold in Type An-1(1)

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Virginia Tech


Let X be the affine flag manifold of Lie type An-1(1) where n ≥ 3 and let Waff be the associated affine Weyl group. The moment graph for X encodes the torus fixed points (which are elements of the affine Weyl group Waff and the torus stable curves in X. Given a fixed point u ∈ Waff and a degree d = (d₀, d₁, ..., dn−1) ∈ ℤ≥0n, the combinatorial curve neighborhood is the set of maximal elements in the moment graph of X which can be reached from u′ ≤ u by a chain of curves of total degree ≤ d. In this thesis we give combinatorial formulas and algorithms for calculating these elements.



Affine Flag Manifolds, Schubert Varieties, Curve Neighborhoods, Moment Graph, Combinatorial Curve Neighborhoods