Families of nested completely regular codes and distance-regular graphs

In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius $\rho$ equal to $3$ or $4$, and are $1/2^i$-th parts, for $i\in\{1,\ldots,u\}$ of binary (respectively, extended binary) Hamming codes of length $n=2^m-1$ (respectively, $2^m$), where $m=2u$. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter $D$ equal to $3$ or $4$ are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive

Gravitational cubic interactions for a massive mixed symmetry gauge field

In a recent paper arXiv:1107.1872 cubic gravitational interactions for a massless mixed symmetry field in AdS space have been constructed. In the current paper we extend these results to the case of massive field. We work in a Fradkin-Vasiliev approach and use frame-like gauge invariant description for massive field which works in (A)dS spaces with arbitrary values of cosmological constant including flat Minkowski space. In this, massless limit in AdS space coincides with the results of arXiv:1107.1872 while we show that it is impossible to switch on gravitational interaction for massless field in dS space.Comment: 13 page

On gravitational interactions for massive higher spins in AdS3AdS_3

In this paper we investigate gravitational interactions of massive higher spin fields in three dimensional $AdS$ space with arbitrary value of cosmological constant including flat Minkowski space. We use frame-like gauge description for such massive fields adopted to three-dimensional case. At first, we carefully analyze the procedure of switching on gravitational interactions in the linear approximation on the example of massive spin-3 field and then proceed with the generalization to the case of arbitrary integer spin field. As a result we construct a cubic interaction vertex linear in spin-2 field and quadratic in higher spin field on $AdS_3$ background. As in the massless case the vertex does not contain any higher derivative corrections to the Lagrangian and/or gauge transformations. Thus, even after switching on gravitational interactions, one can freely consider any massless or partially massless limits as well as the flat one.Comment: 21 pages. Some clarifications and 1 new reference added. Version to appear in the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and Mikhail Vasilie

Conformal self-dual fields

Conformal self-dual fields in flat space-time of even dimension greater than or equal to four are studied. Ordinary-derivative formulation of such fields is developed. Gauge invariant Lagrangian with conventional kinetic terms and corresponding gauge transformations are obtained. Gauge symmetries are realized by involving the Stueckelberg fields. Realization of global conformal symmetries is obtained. Light-cone gauge Lagrangian is found. Also, we demonstrate use of the light-cone gauge for counting of on-shell degrees of freedom of the conformal self-dual fields.Comment: 28 pages, LaTeX-2e, v3: Discussion of realization of conformal algebra symmetries on field strengths added to Sections 3,5. Appendices B,C,D and one reference added. Typos correcte