Deformed Poisson W-algebras of Type A

2019/01/01 by Lachlan Duncan Walker, Lachlan Walker, Walker, Lachlan
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1901.00222

openalex publication_date 2019/01/01 · arxiv created 2019/04/29 · arxiv updated 2019/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the algebraic group SL_l+1(ℂ) we describe a system of positive roots associated to conjugacy classes in its Weyl group. Using this we explicitly describe the algebra of regular functions on certain transverse slices to conjugacy classes in SL_l+1(ℂ) as a polynomial algebra of invariants. These may be viewed as an algebraic group analogue of certain graded parabolic invariants that generate the (graded) W-algebra in type A.

Related

• The Poisson geometry of the conjugation quotient map for simple algebraic groups and deformed Poisson W-algebras
• Conjugacy classes in Weyl groups and q-W algebras
• The structure of q-W algebras
• Deformations of the classical W-algebras associated to D_n, E₆ and G₂
• Deformations of Poisson algebras