Quantization of Special Symplectic Nilpotent Orbits and Normality of their Closures

2013/02/26 by Kayue Daniel Wong, Wong, Kayue Daniel
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1302.6627

17 pages; new version (v7) focuses on symplectic nilpotent orbits only

openalex publication_date 2013/02/26 · arxiv created 2015/12/22 · arxiv updated 2015/12/23 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We study the regular function ring R(O) for all symplectic nilpotent orbits O with even column sizes. We begin by recalling the quantization model for all such orbits by Barbasch using unipotent representations. With this model, we express the multiplicities of fundamental representations appearing in R(O) by a parabolically induced module. Finally, we will use this formula to give a criterion on the normality of the Zariski closure O of O.

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