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Symplectic orthogonality spaces

Robert Piziak
1974 Journal of combinatorial theory. Series A  
Let E be a finite dimensional vector space over the Galois field GF(2). Let lin(E) denote the set of one-dimensional subspaces of E. Let @ be the symplectic inner product on E.  ...  Consider the elements of lin(E) as vertices of a graph, two vertices being connected exactly when they are distinct and orthogonal with respect to 0. This graph is characterized abstractly.  ...  Let (X, 1) be a symplectic orthogonality space. Then there is a symplectic quadratic space (GF(2), E, @) such that (X, I) is isomorphic to (WE), SW.  ... 
doi:10.1016/0097-3165(74)90074-0 fatcat:i45qwdeg6nc7nft25ks6o72hhm

Symplectic space and orthogonal space of n qubits [article]

Jian-Wei Xu
2010 arXiv   pre-print
In the Hilbert space of n qubits, we introduce the symplectic space (n odd) and the orthogonal space (n even) via the spin-flip operator.  ...  the generalized "magic basis" is just the bi-orthonormal basis (that is, the orthonormal basis of both Hilbert space and the orthogonal space ).  ...  Symplectic space and orthogonal space of n qubits  ... 
arXiv:1011.3187v1 fatcat:7ek4sy3tufekfkdfpk7fstvswq

Spacings in Orthogonal and Symplectic Random Matrix Ensembles [article]

Kristina Schubert
2015 arXiv   pre-print
Focussing on orthogonal and symplectic invariant ensembles, we show that the empirical spacing distribution converges in a uniform way.  ...  We consider the universality of the nearest neighbour eigenvalue spacing distribution in invariant random matrix ensembles.  ...  respectively, justifying the full names Gaussian Orthogonal, Unitary and Symplectic Ensembles.  ... 
arXiv:1501.05637v1 fatcat:dzrbhs6xcfhulhyojkfomtbxlu

Minimal rational curves on the moduli spaces of symplectic and orthogonal bundles [article]

Insong Choe, Kiryong Chung, Sanghyeon Lee
2021 arXiv   pre-print
Let ℳ𝒮_C(n,L) and ℳ𝒪_C(n,L) be the moduli spaces of L-valued symplectic and orthogonal bundles respectively, over C of rank n.  ...  We construct rational curves on these moduli spaces which generalize Hecke curves on the moduli space of vector bundles.  ...  (For the sign ±, we take + and − sign in the symplectic and orthogonal case, respectively. The space M should refer to the corresponding space.)  ... 
arXiv:2002.08504v3 fatcat:cc57otknbrh3vcok7htlr6tk5y

Symplectic vs pseudo-orthogonal structure of space-time [article]

Yu. F. Pirogov
2001 arXiv   pre-print
The advantages to consider the ordinary space-time as the symplectic rather than pseudo-orthogonal one are indicated, and the consequences of extending this view to extra space/time dimensions are discussed  ...  Symplectic vs pseudo-orthogonal space-time The space-time, or the world we live in is generally adopted to be (locally) the Minkowski one. Its structure group is the pseudo-orthogonal group SO(1, 3).  ...  The symplectic approach provides an unorthodox alternative to the pseudo-orthogonal space-times and inspires a lot of new opportunities for the physics of extra dimensions.  ... 
arXiv:hep-ph/0110016v1 fatcat:6kcxag2zjze27hfo2kiqckykze

On the moduli spaces of parabolic symplectic orthogonal bundles on curves [article]

Jianping Wang, Xueqing Wen
2021 arXiv   pre-print
We prove that the moduli spaces of parabolic symplectic/orthogonal bundles on a smooth curve are globally F regular type. As a consequence, all higher cohomology of theta line bundle vanish.  ...  Moduli space of semistable parabolic symplectic/orthogonal bundles In this section, we construct the moduli space of semistable parabolic symplectic/orthogonal bundles with fixed parabolic type σ over  ...  with the symplectic/orthogonal structure.  ... 
arXiv:2101.02383v1 fatcat:5g232tuho5gcrm7qrzjqzdxbn4

Hard and soft edge spacing distributions for random matrix ensembles with orthogonal and symplectic symmetry [article]

P.J. Forrester
2006 arXiv   pre-print
at the hard and soft spectrum edges in the cases of orthogonal and symplectic symmetry.  ...  Combining these in the scaled limit with the exact evaluation of the gap probabilities for certain superimposed ensembles with orthogonal symmetry allows for the exact evaluation of the gap probabilities  ...  In the case of spacing distributions in random matrix ensembles with orthogonal or symplectic symmetry, the relationship with Painlevé theory requires further insights.  ... 
arXiv:math-ph/0605022v1 fatcat:4m2w7gywvnclxkrayxt72a4u4e

A stratification on the moduli spaces of symplectic and orthogonal bundles over a curve [article]

Insong Choe, George H. Hitching
2012 arXiv   pre-print
This invariant t defines stratifications on moduli spaces of symplectic and orthogonal bundles.  ...  We also observe some interesting features of orthogonal bundles which do not arise for symplectic bundles, essentially due to the richer topological structure of the moduli space in the orthogonal case  ...  The invariant t(V ) induces stratifications on moduli spaces of semistable symplectic and orthogonal bundles over X.  ... 
arXiv:1204.0834v1 fatcat:e2rip3roufgc3fdzaqofcl4crm

Moduli spaces of orthogonal and symplectic bundles over an algebraic curve

Olivier Serman
2008 Compositio Mathematica  
of orthogonal (respectively symplectic) bundles to the moduli space of all vector bundles overCis an embedding.  ...  Our proof relies on an explicit description of a set of generators for the polynomial invariants on the representation space of a quiver under the action of a product of classical groups.  ...  Orthogonal and symplectic bundles on curves Generators for k[R(Q, α)] Γα Let us go back to the quiver Q and the action of Γ α on its representation space R(Q, α).  ... 
doi:10.1112/s0010437x07003247 fatcat:4hthanjsnvebtfsphwva2b4nju

Partial ovoids and partial spreads in symplectic and orthogonal polar spaces

J. De Beule, A. Klein, K. Metsch, L. Storme
2008 European journal of combinatorics (Print)  
sizes of large maximal partial ovoids and large maximal partial spreads in the classical symplectic and orthogonal polar spaces.  ...  We present improved lower bounds on the sizes of small maximal partial ovoids and small maximal partial spreads in the classical symplectic and orthogonal polar spaces, and improved upper bounds on the  ...  The similar results for the hermitian polar spaces are presented in [11] . We present the results for the classical symplectic and orthogonal polar spaces of rank r ≥ 3.  ... 
doi:10.1016/j.ejc.2007.06.004 fatcat:xcgvvewf3zhpzbmerhxtqzyrce

A stratification on the moduli spaces of symplectic and orthogonal bundles over a curve

Insong Choe, G. H. Hitching
2014 International Journal of Mathematics  
This invariant t defines stratifications on moduli spaces of symplectic and orthogonal bundles.  ...  a symplectic (resp., orthogonal) structure.  ...  The invariant t(V ) induces stratifications on moduli spaces of semistable symplectic and orthogonal bundles over X.  ... 
doi:10.1142/s0129167x14500475 fatcat:6e3buai4sfhbxkamscxllqaify

Cyclic elliptic spreads [article]

W. M. Kantor
2015 arXiv   pre-print
In characteristic 2, an orthogonal vector space is also a symplectic space, and t.s. subspaces are also t.i. subspaces. Orthogonal spreads were defined earlier.  ...  Those papers are based on the fact that a symplectic spread in an Sp(2m, q)-space (with m odd and q even) produces an essentially unique orthogonal spread in an O + (2m + 2, q)-space, while an orthogonal  ... 
arXiv:1512.00861v1 fatcat:zpxclaitsrc2phso5ggt4jinpy

The symplectiness of Maxwell's equations

Wei Sha, Xianliang Wu, Zhixiang Huang, Mingsheng Chen
2008 2008 International Conference on Microwave and Millimeter Wave Technology  
First, we analyze the continuoustime Maxwell's differential equations in free space and verify its time evolution matrix (TEMA) is symplectic-unitary matrix for complex space or symplectic-orthogonal matrix  ...  For the PS approach, the TEMA conserves symplectic-unitary property. For the FD method, the TEMA conserves symplectic-orthogonal property.  ...  Based on Theory 6, the TEMA of Maxwell's equations is a symplectic-orthogonal matrix in real space.  ... 
doi:10.1109/icmmt.2008.4540337 fatcat:msppmodlzbdvjmzwdyowvevtli

Teichmüller space for hyperkähler and symplectic structures

Ekaterina Amerik, Misha Verbitsky
2015 Journal of Geometry and Physics  
The quotient S/_0 is called the Teichmuller space of symplectic (or hyperkahler) structures on M.  ...  This is used to determine the Teichmuller space of symplectic structures of Kahler type on a hyperkahler manifold of maximal holonomy.  ...  The space of symplectic structures The study of the space of symplectic structures was initiated by Moser in [Mos] .  ... 
doi:10.1016/j.geomphys.2015.07.006 fatcat:befuj4zow5hexlgndylztas75e

Products of two involutions in classical groups of characteristic 2

R Gow
1981 Journal of Algebra  
Let k be a field of characteristic 2 and let V be a k-vector space of dimension 2n. A nondefective quadratic form defined on V is a function h: V-t k that satisfies, for U, a in V, c in k,  ...  Since V can clearly be written as an orthogonal direct sum of symplectically indecomposable T-invariant subspaces, the structure of such symplectically indecomposable spaces is of interest.  ...  the complex characters of these three families of finite groups are all real-valued. 583 584 R.GOW ORTHOGONAL DECOMPOSHION OF A SYMPLECTIC SPACE Let T be an element of Sp(2n, V).  ... 
doi:10.1016/0021-8693(81)90198-8 fatcat:czc3ahet2jghvots5s7f2gafhu
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