Three combinatorial formulas for type A quiver polynomials and K-polynomials

Abstract

We provide combinatorial formulas for the multidegree and K-polynomial of an arbitrarily oriented type A quiver locus. These formulas are generalizations of three of Knutson-Miller-Shimozono's formulas from the equioriented setting; in particular, we prove the K-theoretic component formula conjectured by Buch and Rimányi.

v3: significant improvements throughout the article, final version accepted for publication

References in corpus (5)

• Governing Singularities of Schubert Varieties
• On the Cohomological Hall Algebra of Dynkin quivers
• Type A quiver loci and Schubert varieties
• Grothendieck classes of quiver cycles as iterated residues
• Frobenius splitting and Möbius inversion

Cited by in corpus (3)

• Schubert determinantal ideals are Hilbertian
• A family of structure isomorphisms for the Cohomological Hall Algebra of an acyclic quiver
• K-polynomials of type A quiver orbit closures and lacing diagrams