Quantizations of regular functions on nilpotent orbits

2015/05/29 by Ivan Losev, Losev, Ivan
Mathematics · #16G99 (secondary) #17B35 (primary) #53D55 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.AG #math.QA #math.RT #msc:16G99 #msc:17B35 #msc:53D55

paper · pdf · doi:10.48550/arxiv.1505.08048

17 pages

arxiv created 2015/05/29 · openalex publication_date 2015/05/29 · arxiv updated 2015/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the quantizations of the algebras of regular functions on nilpotent orbits. We show that such a quantization always exists and is unique if the orbit is birationally rigid. Further we show that, for special birationally rigid orbits, the quantization has integral central character in all cases but four (one orbit in E₇ and three orbits in E₈). We use this to complete the computation of Goldie ranks for primitive ideals with integral central character for all special nilpotent orbits but one (in E₈). Our main ingredient is results on the geometry of normalizations of the closures of nilpotent orbits by Fu and Namikawa.

Citations

• Quantizations of nilpotent orbits vs 1-dimensional representations of W-algebras
• Generic singularities of nilpotent orbit closures
• On category O for cyclotomic rational Cherednik algebras

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