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N. S. Narasimha Sastry

Publications and source records attributed to N. S. Narasimha Sastry.

5 recordsLinked to original sources
arXiv2020

Split buildings of type F4 in buildings of type E6

A symplectic polarity of a building Δ of type E6 is a polarity whose fixed point structure is a building of type F4 containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type F4). In this paper, we show in a geometric way that every building of type E6 contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type F4 fully embedded in the natural point-line geometry of Δ arises from a symplectic polarity.

math.CO↗
arXiv2017

Ovoidal fibrations in $PG(3,q), q$ even

We prove that, given a partition of the point-set of $PG(3,q), q=2^n >2$, by ovoids $\{θ_i\}^q_{i=0}$ of $PG(3,q)$ and a line $\ell$ of $PG(3,q)$, not tangent to $θ_0$ if $\ell^\perp$ denotes the polar of $\ell$ relative to the symplectic form on $PG(3,q)$ whose isotropic lines are the tangent lines to $θ_0$, then $\ell$ and $\ell^\perp$ are tangent to distinct ovoids $θ_j, θ_k$, both distinct from $θ_0$. This uses the fact that the radical of the linear code generated by the dual duals $\ell\cup \ell^\perp$ of the hyperbolic quadrics , with $\ell$ and $\ell^\perp$ as above, is of codimension $1$

math.GR↗
arXiv2014

On elliptic ovoids and their rosettes in a classical generalized quadrangle of even order

Let Q_0 be the classical generalized quadrangle of order q = 2n arising from a non-degenerate quadratic form in a 5-dimensional vector space defined over a finite field of order q. We consider the rank two geometry X having as points all the elliptic ovoids of Q_0 and as lines the maximal pencils of elliptic ovoids of Q_0 pairwise tangent at the same point. We first prove that X is isomorphic to a 2-fold quotient of the affine generalized quadrangle Q \setminus Q_0 where Q is the classical (q; q^2)-generalized quadrangle admitting Q_0 as a hyperplane. Then, we investigate the collinearity graph Γof X: In particular, we obtain a classification of the cliques of Γproving that they arise either from lines of Q or subgeometries of Q defined over F_2

math.CO↗
arXiv2006

On the order of a non-abelian representation group of a slim dense near hexagon

We show that, if the representation group $R$ of a slim dense near hexagon $S$ is non-abelian, then $R$ is of exponent 4 and $|R|=2^β$, $1+NPdim(S)\leq β\leq 1+dimV(S)$, where $NPdim(S)$ is the near polygon embedding dimension of $S$ and $dimV(S)$ is the dimension of the universal representation module $V(S)$ of $S$. Further, if $β=1+NPdim(S)$, then $R$ is an extraspecial 2-group (Theorem 1.6).

math.CO↗