Combinatorial curve neighborhoods for the affine flag manifold of type A11

Combinatorial Curve Neighborhoods for the Affine Flag Manifold of Type A1

Let X be the affine flag manifold of Lie type A1. 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) ∈ Z≥0, 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 to...

The affine flag variety

the investigation of the relationship between type a and type b personalities and quality of translation

چکیده ندارد.

A Pieri-type Formula for the Equivariant Cohomology of the Flag Manifold

The classical Pieri formula is an explicit rule for determining the coefficients in the expansion s1m · sλ = ∑ c 1,λ sμ , where sν is the Schur polynomial indexed by the partition ν. Since the Schur polynomials represent Schubert classes in the cohomology of the complex Grassmannian, this gives a partial description of the cup product in this cohomology. Pieri’s formula was generalized to the c...

Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type

Fomin and Zelevinsky [9] show that a certain two-parameter family of rational recurrence relations, here called the (b, c) family, possesses the Laurentness property: for all b, c, each term of the (b, c) sequence can be expressed as a Laurent polynomial in the two initial terms. In the case where the positive integers b, c satisfy bc < 4, the recurrence is related to the root systems of finite...