A proof of the continuous Dyson-Maleev representation

Recently Ivanov and Skvortsov introduced continuous Dyson-Maleev (DM) representations of supersymmetric non-linear sigma models and motivated that these representations are non-perturbatively exact. Basic to all continuous DM representations of this kind are certain identities for integrals over hermitian (super)symmetric spaces. We establish these basic identities rigorously in the non-super case.Comment: 13 page

Basic representations of quantum current algebras in higher genus

We construct level 1 basic representations of the quantized current algebras associated to higher genus algebraic curves using one free field. We also clarify the relation between the elliptic current algebras of the papers [EF] and [JKOS].Comment: 11 pages, typos and acknowledge adde

Complete Cubic and Quartic Couplings of 16 and 16ˉ\bar {16} in SO(10) Unification

A recently derived basic theorem on the decomposition of SO(2N) vertices is used to obtain a complete analytic determination of all SO(10) invariant cubic superpotential couplings involving $16_{\pm}$ semispinors of SO(10) chirality $\pm$ and tensor representations. In addition to the superpotential couplings computed previously using the basic theorem involving the 10, 120 and $\bar{126}$ tensor representations we compute here couplings involving the 1, 45 and 210 dimensional tensor representations, i.e., we compute the $\bar{16}_{\mp}16_{\pm}1$,$\bar{16}_{\mp}16_{\pm}45$ and $\bar{16}_{\mp}16_{\pm}210$ Higgs couplings in the superpotential. A complete determination of dimension five operators in the superpotential arising from the mediation of the 1, 45 and 210 dimensional representations is also given. The vector couplings $\bar{16}_{\pm}16_{\pm}1$, $\bar{16}_{\pm}16_{\pm}45$ and $\bar{16}_{\pm}16_{\pm}210$ are also analyzed. The role of large tensor representations and the possible application of results derived here in model building are discussed.Comment: 21 pages, Latex. Revised version to appear in Nuclear Physics

On the Fourier analysis of operators on the torus

Basic properties of Fourier integral operators on the torus are studied by using the global representations by Fourier series instead of local representations. The results can be applied to weakly hyperbolic partial differential equations

Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe