In this note we offer a short summary of some recent results, to be contained in a forthcoming paper [4], on projective caps and linear error correcting codes arising from the Grassmann embedding ε k of an orthogonal Grassmannian ∆k. More precisely, we consider the codes arising from the projective system determined by ε k (∆k) and determine some of their parameters. We also investigate special...

The geodesic motion of pseudo-classical spinning particles in Euclidean Taub-NUT space is analysed. The constants of motion are expressed in terms of Killing-Yano tensors. Some previous results from the literature are corrected. PACS number(s): 04.20.Jb, 02.40.-K The con guration space of spinning particles (spinning space) is an supersymmetric extension of an ordinary Riemannian manifold, para...

The spin degrees of freedom for the relativistic particle are described by either Lorentz group variables (classically) or Grassmann variables (pseudo-classically). The relationship between those two descriptions are given. In doing that, appropriate constraints are constructed to put into the lagrangian. Especially a natural relation of Lorentz group variables and Grassmann variables is obtain...

We show that the BV (Batalin Vilkovisky) action, formulated with an extended BRST symmetry (including the shift symmetry), is also invariant under an extended anti-BRST transformation (where the antifields are the parameters of the transformation), when the gauge fixing Lagrangian is both BRST and anti-BRST invariant. We show that for a general gauge fixing Lagrangian, the BV action can be writ...

In this note, we characterize the Grassmann embedding of H(q), q even, as the unique full embedding of H(q) in PG(12, q) for which each ideal line of H(q) is contained in a plane. In particular, we show that no such embedding exists for H(q), with q odd. As a corollary, we can classify all full solid polarized embeddings of H(q) in PG(12, q); they are necessarily Grassmann embeddings of H(q), w...

We investigate a generalization of Brockett’s celebrated double bracket flow that is closely related to matrix Riccati differential equations. Using known results on the classification of transitive Lie group actions on homogeneous spaces, necessary and sufficient conditions for accessibility of the generalized double bracket flow on Grassmann manifolds are derived. This leads to sufficient Lie...

We study subsets of Grassmann varieties G(l, m) over a field F , such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study the linear spans of, and in case of positive characteristic, the number of Fq-rational points on such unions. Moreover we study a geometric duality of such unions, and give a combinatorial interpretation of this duality. We discuss the ma...

Supersymmetry transformations may be represented by unitary operators in a formulation of supersymmetry without numbers that anti-commute. The physical relevance of this formulation hinges on whether or not one may add states of even and odd fermion number, a question which soon may be settled by experiment.