Séminaire Lotharingien de Combinatoire, 86B.70 (2022), 12 pp.
Andy Wilson
The Elliptic Hall Algebra Element Qm,nk(1)
Abstract.
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 and conjecture that this function is equal (up to a constant) to the elliptic Hall algebra operator Qm,n composed k times and applied to 1. 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.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.