Proof of Kac and Rudakov's Conjecture on Generalized Verma Module over Lie Superalgebra E(5,10)

2012/11/20 by Yufeng Zhao, Zhao, Yufeng
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #representaion theory

paper · pdf · doi:10.48550/arxiv.1211.4638

34 pages

arxiv created 2012/11/20 · openalex publication_date 2012/11/20 · arxiv updated 2012/11/21 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

The exceptional infinite-dimensional linearly compact simple Lie superalgebra E(5,10), which Kac believes, is the algebra of symmetries of the SU₅ Grand Unified Model. In this paper, we give a proof of Kac and Rudakov's conjecture about the classification of all the degenerate generalized Verma module over E(5,10). Also, we work out all the nontrivial singular vectors degree by degree. It is a potential that the representation theory of E(5,10) will shed new light on various features of the the SU₅ Grand unified model.

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