2025/02/19 by Hunter Dinkins, Dinkins, Hunter, Jang, Jiwu · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2502.13937
openalex publication_date 2025/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the quasimap vertex functions of type D Nakajima quiver varieties. When the quiver varieties have isolated torus fixed points, we compute the coefficients of the vertex functions in the K-theoretic fixed point basis. We also give an explicit combinatorial description of zero-dimensional type D quiver varieties and their vertex functions using the combinatorics of minuscule posets. Using Macdonald polynomials, we prove that these vertex functions can be expressed as products of q-binomial functions, which proves a degeneration of the conjectured 3d mirror symmetry of vertex functions. We provide an interpretation of type D spin vertex functions as the partition functions of the half-space Macdonald processes of Barraquand, Borodin, and Corwin. This hints that the geometry of quiver varieties may provide new examples of integrable probabilistic models.