Quiver coefficients are Schubert structure constants

Details Quiver coefficients are Schubert structure constants Quiver coefficients are Schubert structure constants

2003-11-21

arxiv.org/abs/math/0311390v1

Mathematical Research Letters, Volume 12, Issue 4, 567-574 (2005).

Mathematics

Combinatorics

7 pages, 5 figures

Scientific paper

We give an explicit natural identification between the quiver coefficients of Buch and Fulton, decomposition coefficients for Schubert polynomials, and the Schubert structure constants for flag manifolds. This is also achieved in K-theory where we give a direct argument that the decomposition coefficients have alternating signs, based on a theorem of Brion, which then implies that the quiver coefficients have alternating signs. Our identification shows that known combinatorial formulas for the latter two numbers give formulas for the quiver coefficients.

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