Formal confluence of quantum differential operators

Bernard Le Stum (1) , Adolfo Quirós (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Departamento de Matemáticas

We prove that a usual differential operator is formally the limit of quantum differential operators. For this purpose, we introduce the notion of twisted differential operator of infinite level and prove that, formally, such an object is independent of the choice of the twist. Our method provides explicit formulas.

Mots clés: q-difference; differential operator; Confluence

Domaines: Géométrie algébrique [math.AG]

Bernard Le Stum, Adolfo Quirós. Formal confluence of quantum differential operators. Pacific Journal of Mathematics, 2018, 292 (2), pp.427-478. ⟨10.2140/pjm.2018.292.427⟩. ⟨hal-01158436⟩