scholarly journals Nearly all subspaces of a classical polar space arise from its universal embedding

2021 ◽  
Author(s):  
I. Cardinali ◽  
L. Giuzzi ◽  
A. Pasini
Keyword(s):  
Polar Space ◽  
Universal Embedding

The hyperplanes of DW(5,F) arising from the Grassmann embedding

2017 ◽  
Vol 32 ◽  
pp. 1-14 ◽  
Author(s):  
Bart De Bruyn ◽  
Mariusz Kwiatkowski
Keyword(s):  
Main Tool ◽  
Complete Classification ◽  
Polar Space ◽  
Equivalence Classes ◽  
Dual Polar Space ◽  
Characteristic 2 ◽  
Universal Embedding ◽  
Symplectic Vector Space ◽  
Dimensional Module

The hyperplanes of the symplectic dual polar space DW(5; F) that arise from the Grassmann embedding have been classied in [B.N. Cooperstein and B. De Bruyn. Points and hyperplanes of the universal embedding space of the dual polar space DW(5; q), q odd. Michigan Math. J., 58:195{212, 2009.] in case F is a finite field of odd characteristic, and in [B. De Bruyn. Hyperplanes of DW(5;K) with K a perfect eld of characteristic 2. J. Algebraic Combin., 30:567{584, 2009.] in case F is a perfect eld of characteristic 2. In the present paper, these classifications are extended to arbitrary fields. In the case of characteristic 2 however, it was not possible to provide a complete classification. The main tool in the proof is the classification of the quasi-Sp(V; f)-equivalence classes of trivectors of a 6-dimensional symplectic vector space (V; f) obtained in [B. De Bruyn and M. Kwiatkowski. A 14-dimensional module for the symplectic group: orbits on vectors. Comm. Algebra,43:4553{4569, 2015.

scholarly journals The Universal Embedding of the Near Polygon ${\Bbb G}_n$

10.37236/957 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Bart De Bruyn
Keyword(s):  
Automorphism Group ◽  
Polar Space ◽  
Near Polygon ◽  
Dual Polar Space ◽  
Large Automorphism Group ◽  
Universal Embedding

In an earlier paper, we showed that the dual polar space $DH(2n-1,4)$, $n \geq 2$, has a sub near-$2n$-gon ${\Bbb G}_n$ with a large automorphism group. In this paper, we determine the absolutely universal embedding of this near polygon. We show that the generating and embedding ranks of ${\Bbb G}_n$ are equal to ${2n \choose n}$. We also show that the absolutely universal embedding of ${\Bbb G}_n$ is the unique full polarized embedding of this near polygon.

scholarly journals Calculating the Dimension of the Universal Embedding of the Symplectic Dual Polar Space using Languages

10.37236/9754 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Carlos Segovia ◽  
Monika Winklmeier
Keyword(s):  
Polar Space ◽  
Symplectic Space ◽  
Alternative Proof ◽  
Isotropic Subspace ◽  
Dual Polar Space ◽  
Standard Order ◽  
Isotropic Subspaces ◽  
Universal Embedding ◽  
Totally Isotropic Subspaces ◽  
Symplectic Dual Polar Space

The main result of this paper is the construction of a bijection of the set of words in so-called standard order of length $n$ formed by four different letters and the set $\mathcal{N}^n$ of all subspaces of a fixed $n$-dimensional maximal isotropic subspace of the $2n$-dimensional symplectic space $V$ over $\mathbb{F}_2$ which are not maximal in a certain sense. Since the number of different words in standard order is known, this gives an alternative proof for the formula of the dimension of the universal embedding of a symplectic dual polar space $\mathcal{G}_n$. Along the way, we give formulas for the number of all $n$- and $(n-1)$-dimensional totally isotropic subspaces of $V$.

scholarly journals Fully abstract compilation via universal embedding

2016 ◽  
Vol 51 (9) ◽  
pp. 103-116 ◽  
Author(s):  
Max S. New ◽  
William J. Bowman ◽  
Amal Ahmed
Keyword(s):  
Universal Embedding

A plastically bendable and polar organic crystal

CrystEngComm ◽  
2021 ◽  
Author(s):  
Sotaro Kusumoto ◽  
Akira Sugimoto ◽  
Daisuke Kosumi ◽  
Yang Kim ◽  
Yoshihiro Sekine ◽  
...  
Keyword(s):  
Mechanical Stress ◽  
Polar Space ◽  
Organic Crystal ◽  
Space Group ◽  
High Dielectric

In this communication, an organic crystal of the polar space group Pc that is capable of plastically bending in response to external mechanical stress is reported, and its high dielectric...

Sign in / Sign up

Export Citation Format

Share Document