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In this paper, we develop a new method for constructing $m$-ovoids in the symplectic polar space $W(2r-1,q)$ from some strongly regular Cayley graphs in cite{Brouwer1999Journal}. Using this method, we obtain many new $m$-ovoids which can not be derived by field reduction.
Veldkamp polygons are certain graphs $Gamma=(V,E)$ such that for each $vin V$, $Gamma_v$ is endowed with a symmetric anti-reflexive relation $equiv_v$. These relations are all trivial if and only if $Gamma$ is a thick generalized polygon. A Veldkamp
The adjacency matrix of a symplectic dual polar graph restricted to the eigenspaces of an abelian automorphism subgroup is shown to act as the adjacency matrix of a weighted subspace lattice. The connection between the latter and $U_q(sl_2)$ is used
In this paper, which is a sequel to cite{part1}, we proceed with our study of covers and decomposition laws for geometries related to generalized quadrangles. In particular, we obtain a higher decomposition law for all Kantor-Knuth generalized quadra
We prove that a polar foliation of codimension at least three in an irreducible compact symmetric space is hyperpolar, unless the symmetric space has rank one. For reducible symmetric spaces of compact type, we derive decomposition results for polar foliations.
For a compact Poisson-Lie group $K$, the homogeneous space $K/T$ carries a family of symplectic forms $omega_xi^s$, where $xi in mathfrak{t}^*_+$ is in the positive Weyl chamber and $s in mathbb{R}$. The symplectic form $omega_xi^0$ is identified wit