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

Yufeng Zhao

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

Representation Theory 2012-11-21 v1 Quantum Algebra

Authors: Yufeng Zhao

Abstract

The exceptional infinite-dimensional linearly compact simple Lie superalgebra ${E}(5,10)$ , which Kac believes, is the algebra of symmetries of the ${SU}_{5}$ 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 ${SU}_{5}$ Grand unified model.

Keywords

Lie superalgebra E(5,10) generalized Verma module Kac-Rudakov conjecture singular vectors representation theory Grand Unified Model

Cite

@article{arxiv.1211.4638,
  title  = {Proof of Kac and Rudakov's Conjecture on Generalized Verma Module over Lie Superalgebra E(5,10)},
  author = {Yufeng Zhao},
  journal= {arXiv preprint arXiv:1211.4638},
  year   = {2012}
}

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34 pages

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

Abstract

Keywords

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