Notes on higher-spin algebras: minimal representations and structure constants
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Publication:270724
DOI10.1007/JHEP05(2014)103zbMATH Open1333.81188arXiv1401.7977MaRDI QIDQ270724
Author name not available (Why is that?)
Publication date: 7 April 2016
Published in: (Search for Journal in Brave)
Abstract: The higher-spin (HS) algebras so far known can be interpreted as the symmetries of the minimal representation of the isometry algebra. After discussing this connection briefly, we generalize this concept to any classical Lie algebras and consider the corresponding HS algebras. For sp(2N) and so(N), the minimal representations are unique so we get unique HS algebras. For sl(N), the minimal representation has one-parameter family, so does the corresponding HS algebra. The so(N) HS algebra is what underlies the Vasiliev theory while the sl(2) one coincides with the 3D HS algebra hs[lambda]. Finally, we derive the explicit expression of the structure constant of these algebras --- more precisely, their bilinear and trilinear forms. Several consistency checks are carried out for our results.
Full work available at URL: https://arxiv.org/abs/1401.7977
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