Blocking sets in line Grassmannians

Affine Tallini Sets and Grassmannians

In 1982/1983 A. Bichara and F. Mazzocca characterized the Grassmann space Gr(h,A) of index h of an affine space A of dimension at least 3 over a skew–field K by means of the intersection properties of the three disjoint families of maximal singular subspaces of Gr(h,A) and, till now, their result represents the only known characterization of Gr(h,A). If K is a commutative field and A has finite...

Enumerative Coding for Line Polar Grassmannians

Codes arising from Grassmannians have been widely investigated, both as generalization of Reed–Muller codes and for applications to network coding. Recently we introduced some new codes, arising from Polar Grassmannians, namely the set of all subspaces of a vector space F q which are totally singular with respect to a given non-degenerate quadratic form. The aim of the present paper is to prese...

Intertwining Operators between Line Bundles on Grassmannians

Let G = GL(n, F ) where F is a local field of arbitrary characteristic, and let π1, π2 be representations induced from characters of two maximal parabolic subgroups P1, P2. We explicitly determine the space HomG (π1, π2) of intertwining operators and prove that it has dimension ≤ 1 in all cases.

Blocking sets in handcuffed designs

In this paper we determine the spectrum of possible cardinalities of a blocking set in a H(v,3,A) and in a H(v,4,1). Moreover we construct, for each admissible ~9, a H(v,3,1) without blocking sets. Introduction A handcuffed design with parameters v, k, A, or for short an H(v,k,A), consists of a set of ordered k-subsets of a v-set, called handcuffed blocks. In a block (a., a z ' ... ,a!:) each e...

Blocking sets in chain geometries