Quasi-split symmetric pairs of 𝑈(𝔰𝔩_{𝔫}) and Steinberg varieties of classical type

We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type A n − 1 A_{n-1} . This is obtained inside the limit of a projective system of Borel-Moore homologies of the Steinberg varieties of n n -step isotropic flag varieties. Arising from the construction are a basis of homological origin for the idempotent form and a geometric realization of rational modules.

On-shell gauge invariant three-point fermion and boson amplitudes

A polynomial basis for parity-even three-point amplitudes of higher-spin massless fermions and bosons are derived in four-dimensional space–time from first principles. This basis can be used to construct three-point amplitudes of polarizations of any rank. The results are presented using polarization tensors and tensor-spinors, which is convenient when they are applied to Lagrangian construction.

BRST LAGRANGIAN CONSTRUCTION FOR SPIN-$\frac{3}{2}$ FIELD IN EINSTEIN SPACE

We explore a hidden possibility of BRST approach to higher spin field theory to obtain a consistent Lagrangian for massive spin-[Formula: see text] field in Einstein space of arbitrary d ≥ 3 dimension. Also, we prove that in the space under consideration the propagation of spin-[Formula: see text] field is hyperbolic and causal.

BRST APPROACH TO LAGRANGIAN FORMULATION OF BOSONIC TOTALLY ANTISYMMETRIC TENSOR FIELDS IN CURVED SPACE

We apply the BRST approach, previously developed for higher spin field theories, to gauge-invariant Lagrangian construction for antisymmetric massive and massless bosonic fields in arbitrary d-dimensional curved space. The obtained theories are reducible gauge models both in massless and massive cases and the order of reducibility grows with the value of the rank of the antisymmetric field. In both cases the Lagrangians contain the sets of auxiliary fields and possess more rich gauge symmetry in comparison with standard Lagrangian formulation for the antisymmetric fields. This serves as an additional demonstration of universality of the BRST approach for Lagrangian constructions in various field models.