相关论文: Massless Conformal Fields in Ten Dimensions, Minim…
We extend our earlier work on the minimal unitary representation of $SO(d,2)$ and its deformations for $d=4,5$ and $6$ to arbitrary dimensions $d$. We show that there is a one-to-one correspondence between the minrep of $SO(d,2)$ and its…
We study the minimal unitary representation (minrep) of SO(6,2) over an Hilbert space of functions of five variables, obtained by quantizing its quasiconformal realization. The minrep of SO(6,2), which coincides with the minrep of SO*(8)…
We study the minimal unitary representation (minrep) of SO(4,2) over an Hilbert space of functions of three variables, obtained by quantizing its quasiconformal action on a five dimensional space. The minrep of SO(4,2), which coincides with…
Massless conformal scalar field in six dimensions corresponds to the minimal unitary representation (minrep) of the conformal group SO(6,2). This minrep admits a family of deformations labelled by the spin t of an SU(2)_T group, which is…
Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of…
Minimal unitary representation of SO*(8) = SO(6,2) realized over the Hilbert space of functions of five variables and its deformations labeled by the spin t of an SU(2) subgroup correspond to massless conformal fields in six dimensions as…
We study the minimal unitary representation (minrep) of SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2) describes a massless conformal scalar…
Massless conformal scalar field in d=4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2,2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The…
We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E_{8(-24)} in SU*(8) as well as…
We review the novel quasiconformal realizations of exceptional U-duality groups whose "quantization" lead directly to their minimal unitary irreducible representations. The group $E_{8(8)}$ can be realized as a quasiconformal group in the…
We compute the supersymmetry constraints on the R^4 type corrections in maximal supergravity in dimension 8, 6, 4 and 3, and determine the tensorial differential equations satisfied by the function of the scalar fields multiplying the R^4…
The quasiconformal method provides us with a unified approach to the construction of minimal unitary representations (minrep) of noncompact groups, their deformations as well as their supersymmetric extensions. We review the quasiconformal…
We study the minimal unitary representations of non-compact groups and supergroups obtained by quantization of their geometric realizations as quasi-conformal groups and supergroups. The quasi-conformal groups G leave generalized…
After reviewing the underlying algebraic structures we give a unified realization of split exceptional groups F_{4(4)},E_{6(6)}, E_{7(7)}, E_{8(8)} and of SO(n+3,m+3) as quasiconformal groups that is covariant with respect to their…
The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2), combining rigorous representation-theoretic analysis with…
We consider polynomial deformations of Lie superalgebras and their representations. For the class A(n-1,0) ~ sl(n/1), we identify families of superalgebras of quadratic and cubic type, consistent with Jacobi identities. For such deformed…
We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian…
We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A…
Respecting the group theoretical approach, it is discussed that the linear conformal gravity can be written in terms of a mixed symmetry tensor field of rank-3 \cite{binegar}. Following this path, related field equation was obtained in de…
In the present paper we construct all short representation of $so(3,2)$ with the $sl(2,\mathbb{C})$ symmetry made manifest due to the use of $sl(2,\mathbb{C})$ spinors. This construction has a natural connection to the spinor-helicity…