Geodesic
Higher-Rank Conformal Fields in the $Sp(2M)$-Symmetric Generalized Space-Time
Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 1, pp. 35-65

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We study various $Sp(2M)$-invariant field equations corresponding to rank-$r$ tensor products of the Fock (singleton) representation of $Sp(2M)$. These equations describe localization on “branes” of different dimensions embedded in the generalized space-time $\mathcal M_M$ with matrix (i.e., “central charge”) coordinates. We consider the case of a bilinear tensor product in detail and show that the conserved currents built from bilinears of rank-1 fields in satisfy the field equations for rank-2 fields in $\mathcal M_M$. We also show that rank-2 fields in $\mathcal M_M$ are equivalent to rank-1 fields in $\mathcal M_{2M}$.
Keywords: higher-spin fields, higher symmetries. 
@article{TMF_2005_145_1_a1,
     author = {M. A. Vasiliev and O. A. Gelfond},
     title = {Higher-Rank {Conformal} {Fields} in the $Sp(2M)${-Symmetric} {Generalized} {Space-Time}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {35--65},
     publisher = {mathdoc},
     volume = {145},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_145_1_a1/}
}
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M. A. Vasiliev; O. A. Gelfond. Higher-Rank Conformal Fields in the $Sp(2M)$-Symmetric Generalized Space-Time. Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 1, pp. 35-65. http://geodesic.mathdoc.fr/item/TMF_2005_145_1_a1/