Generators of the quantum finite W-algebras in type A

2018/06/08 by De Sole, Alberto, Fedele, Laura, Valeri, Daniele
#17B08 #17B35 #17B63 #17B80 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1806.03233

Abstract

We prove a conjecture proposed in [DSKV16] describing the Lax type operator L(z) for the quantum finite W-algebras of gl_N in terms of a PBW generating system for the W-algebra. In doing so, we extend this result to an arbitrary good grading and an arbitrary isotropic subspace of g[1/2].

Related

• Weak generators of W-algebras for type A
• A Lax type operator for quantum finite W-algebras
• W-algebras via Lax type operators
• Finite W-algebra invariants via Lax type operators
• Generalized finite and affine W-algebras in type A