A presentation of the deformed W_{1+\infty} algebra

TL;DR

This paper presents a detailed algebraic description of the deformed W_{1+ abla} algebra, connecting it to cohomological Hall algebras and degenerate double affine Hecke algebras, expanding understanding of their structure.

Contribution

It provides a generators and relations presentation of the deformed W_{1+ abla} algebra, linking it to known algebraic structures like Hall algebras and Hecke algebras.

Findings

Provides explicit generators and relations for the algebra

Establishes connections with cohomological Hall algebras

Links to degenerate double affine Hecke algebras

Abstract

We provide a generators and relation description of the deformed W_{1+\infty}-algebra introduced in previous joint work of E. Vasserot and the second author. This gives a presentation of the (spherical) cohomological Hall algebra of the one-loop quiver, or alternatively of the spherical degenerate double affine Hecke algebra of GL(\infty).