Geometric construction of crystal bases for quantum generalized Kac-Moody algebras

TL;DR

This paper presents a geometric method to construct crystal bases for quantum generalized Kac-Moody algebras using irreducible components of specific Lagrangian subvarieties in quiver representation spaces.

Contribution

It introduces a novel geometric realization of the crystal $B( abla)$ for quantum generalized Kac-Moody algebras through Lagrangian subvarieties.

Findings

Realization of crystal bases via geometric methods.

Connection between Lagrangian subvarieties and crystal structures.

Framework applicable to quantum generalized Kac-Moody algebras.

Abstract

We provide a geometric realization of the crystal $B(\infty)$ for quantum generalized Kac-Moody algebras in terms of the irreducible components of certain Lagrangian subvarieties in the representation spaces of a quiver.