In this paper we introduce and study line Hermitian Grassmann codes as those subcodes of the Grassmann codes associated to the $2$-Grassmannian of a Hermitian polar space defined over a finite field of square order. In particular, we determine their parameters and characterize the words of minimum weight.

To each coherent configuration (scheme) C and positive integer m we associate a natural scheme Ĉ(m) on the m-fold Cartesian product of the point set of C having the same automorphism group as C. Using this construction we define and study two positive integers: the separability number s(C) and the Schurity number t(C) of C. It turns out that s(C) ≤ m iff C is uniquely determined up to isomorphi...

We prove that the m-generated Grassmann algebra can be embedded into a 2 × 2 matrix algebra over a factor of a commutative polynomial algebra in m indeterminates. Cayley–Hamilton and standard identities for n× n matrices over the m-generated Grassmann algebra are derived from this embedding. Other related embedding results are also presented.

Conservation of statistics requires that fermions be coupled to Grassmann external sources. Correspondingly, conservation of statistics requires that parabosons, parafermions and quons be coupled to external sources that are the appropriate generalizations of Grassmann numbers. Supported in part by a Semester Research Grant from the University of Maryland, College Park and by the National Scien...

In this paper we determine the minimum distance of orthogonal line-Grassmann codes for q even. The case q odd was solved in [3]. We also show that for q even all minimum weight codewords are equivalent and that symplectic line-Grassmann codes are proper subcodes of codimension 2n of the orthogonal ones.

A supersymmetric D = 1, N = 1 model with a Grassmann-odd Lagrangian is proposed which, in contrast to the model with an even Lagrangian, contains not only a kinetic term but also an interaction term for the coordinates entering into one real scalar Grassmann-even (bosonic) superfield.

We describe how the loop group maps corresponding to special submanifolds associated to integrable systems may be thought of as certain Grassmann submanifolds of infinite dimensional homogeneous spaces. In general, the associated families of special submanifolds are certain Grassmann submanifolds. An example is given from the recent article [2].

It is shown that the integrability conditions of the equations satisfied by the local Frenet frame associated with a holomorphic curve in a complex Grassmann manifold coincide with a special class of nonabelian Toda equations. A local moving frame of a holomorphic immersion of a Riemann surface into a complex Grassmann manifold is constructed and the corresponding connection coefficients are ca...