On factorization algebras arising in the quantum geometric Langlands theory

TL;DR

This paper explores the construction of factorization algebras related to quantum groups within the quantum geometric Langlands framework, revealing their geometric origins via Zastava spaces and twisted sheaves.

Contribution

It demonstrates that the factorization algebra associated with Lusztig's quantum group can be realized as a direct image of a twisted Whittaker sheaf on the Zastava space, connecting algebraic and geometric perspectives.

Findings

Factorization algebra linked to Lusztig's quantum group derived from Zastava space

Establishment of geometric realization of quantum group-related factorization algebras

Connection between quantum groups and twisted sheaves on configuration spaces

Abstract

We study factorization algebras on configuration spaces of points on the curved, colored by elements of the root lattice. We show that the factorization algebra attached to Lusztig's quantum group can be obtained as a direct image of a twisted Whittaker sheaf on the Zastava space.