Quantum Langlands duality of representations of W-algebras

Abstract

We prove duality isomorphisms of certain representations of W-algebras which play an essential role in the quantum geometric Langlands Program and some related results.

arXiv comment30 pages, to appear in Compositio Mathematica

References in corpus (4)

• Vertex Algebras and Algebraic Curves
• The Relation between Quantum W algebras and Lie algebras
• W-algebras as coset vertex algebras
• Two-sided BGG resolutions of admissible representations

Cited by in corpus (10)

• Trialities of $\mathcal{W}$-algebras
• Universal two-parameter ${\mathcal{W}}_{\infty }$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots ,N)$
• Subregular W-algebras of type A
• Rationality of the exceptional W-algebras ${\mathcal{W}}_k({\mathfrak{sp}}_4,f_{subreg})$ associated with subregular nilpotent elements of ${\mathfrak{sp}}_4$
• Simplicity of higher rank triplet W-algebras
• On the structure of W-algebras in type A
• Ordinary modules for vertex algebras of ${\mathfrak{osp}}_{1|2n}$
• Cosets from equivariant W-algebras
• Orthosymplectic Feigin-Semikhatov duality
• Feigin-Semikhatov conjecture and related topics