Nonabelian shift operators and shifted Yangians

TL;DR

This paper introduces nonabelian shift operators in enumerative geometry, linking it to automorphic forms and providing new insights into quantized Coulomb branch algebras, including a proof related to affine Grassmannians and shifted Yangians.

Contribution

It develops nonabelian shift operators in enumerative geometry and applies them to connect geometric automorphic forms with Coulomb branch algebras, offering new proofs and insights.

Findings

Equivariant convolution homology of affine Grassmannian is a quotient of a shifted Yangian.

Nonabelian shift operators strengthen the analogy between enumerative geometry and automorphic forms.

New proof that relates affine Grassmannian homology to shifted Yangians.

Abstract

We introduce nonabelian analogs of shift operators in the enumerative theory of quasimaps. We apply them on the one hand to strengthen the emerging analogy between enumerative geometry and the geometric theory of automorphic forms, and on the other hand to obtain results about quantized Coulomb branch algebras. In particular, we find a short and direct proof that the equivariant convolution homology of the affine Grassmannian of $GL_n$ is a quotient of a shifted Yangian.