N. S. Narasimha Sastry

intersection Pattern of the Classical Ovoids in Symplectic 3-Space of Even Order

For s = 2e, e > 1 odd, we determine how the copies of the Suzuki group Sz(s) in the symplectic group Sp(4, s) intersect. Using this information we determine how the classical ovoids in symplectic 3-space W(s) meet and obtain a complete set of double coset representatives of Sz(s) in Sp(4, s). We also note that the permutation representation of Sp(4, s) on the cosets of Sz(s) is multiplicity free, and its irreducible constituents are explicitly determined. Indeed, we show that the complex Hecke algebra of this permutation representation is isomorphic to the center of the complex group algebra of Sz(s). A combinatorial offshoot of this study is the construction of several new series of Buekenhout diagram geometries of type which are embedded as subgeometries of miquelian and Suzuki-Tits inversive planes.

Completely Bounded Modules and Associated Extremal Problems

In this paper we continue our study of certain finite dimensional Hilbert modules over the function algebra A(Ω), Ω ⊆ Cm. We show that these modules are always completely bounded with the bound obtained as the matrix valued analogue of a certain scalar valued extremal problem. In particular, we obtain a necessary and sufficient condition for our module to be completely contractive. We produce a contractive module CNm over A(Bm) such that it is completely bounded with the complete bound equal to √m; that is, CNm is not completely contractive.

A characterization of finite symplectic polar spaces of odd prime order

A sufficient condition for the representation group for a nonabelian representation (Definition 1.1) of a finite partial linear space to be a finite p-group is given (Theorem 2.9). We characterize finite symplectic polar spaces of rank r at least two and of odd prime order p as the only finite polar spaces of rank at least two and of prime order admitting nonabelian representations. The representation group of such a polar space is an extraspecial p-group of order p^1^+^2^r and of exponent p (Theorems 1.5 and 1.6).

Codes from Veronese and Segre Embeddings and Hamada's Formula

In this article we study the codes given by l hypersurfaces in Pnq to obtain a new formula for the dimension of codes given by (n?l) flats. We also obtain a new formula for the dimension of the ? th order generalized Reed?Muller code and describe the code given by the hyperplane intersections of the Segre embedding of Pnq×Pmq.

On the doubly transitive permutation representations of Sp(2n,F2)

Abstract Each symplectic group over the field of two elements has two exceptional doubly transitive actions on sets of quadratic forms on the defining symplectic vector space. This paper studies the associated 2-modular permutation modules. Filtrations of these modules are constructed which have subquotients which are modules for the symplectic group over an algebraically closed field of characteristic 2 and which, as such, have filtrations by Weyl modules and dual Weyl modules having fundamental highest weights. These Weyl modules have known submodule structures. It is further shown that the submodule structures of the Weyl modules are unchanged when restricted to the finite subgroups Sp(2 n ,2) and O ± (2 n ,2).

Codes Associated with Nondegenerate Quadrics of a Symplectic Space of Even Order

This paper studies the incidence relation between the points and quadrics in the projective space of a symplectic vector space over a field of even order. The 2-rank of the incidence matrix is determined. This is achieved by viewing the code generated by incidence vectors as a module for the symplectic group and applying the 2-modular representation theory of this group. The radical series of this module is also described.

Binary codes of the symplectic generalized quadrangle of even order

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Algebraic Codes and Geometry of Some Classical Generalized Polygons

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