2022/05/31 by Wilson, Andy
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2206.00075
openalex publication_date 2022/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose M and N are positive integers and let k = gcd(M, N), m = M/k, and n=N/k. We define a symmetric function LM,N as a weighted sum over certain tuples of lattice paths. We show that LM,N satisfies a generalization of Mellit and Hogancamp's recursion for the triply-graded Khovanov--Rozansky homology of the M,N-torus link. As a corollary, we obtain the triply-graded Khovanov--Rozansky homology of the M,N-torus link as a specialization of LM,N. We conjecture that LM,N is equal (up to a constant) to the elliptic Hall algebra operator Qm,n composed k times and applied to 1.