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Symplectic orthogonality spaces

1974
*
Journal of combinatorial theory. Series A
*

Let E be a finite dimensional vector

doi:10.1016/0097-3165(74)90074-0
fatcat:i45qwdeg6nc7nft25ks6o72hhm
*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. ...##
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Symplectic space and orthogonal space of n qubits
[article]

2010
*
arXiv
*
pre-print

In the Hilbert

arXiv:1011.3187v1
fatcat:7ek4sy3tufekfkdfpk7fstvswq
*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 ...##
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Spacings in Orthogonal and Symplectic Random Matrix Ensembles
[article]

2015
*
arXiv
*
pre-print

Focussing on

arXiv:1501.05637v1
fatcat:dzrbhs6xcfhulhyojkfomtbxlu
*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. ...##
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Minimal rational curves on the moduli spaces of symplectic and orthogonal bundles
[article]

2021
*
arXiv
*
pre-print

Let ℳ𝒮_C(n,L) and ℳ𝒪_C(n,L) be the moduli

arXiv:2002.08504v3
fatcat:cc57otknbrh3vcok7htlr6tk5y
*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*.) ...##
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Symplectic vs pseudo-orthogonal structure of space-time
[article]

2001
*
arXiv
*
pre-print

The advantages to consider the ordinary

arXiv:hep-ph/0110016v1
fatcat:6kcxag2zjze27hfo2kiqckykze
*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. ...##
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On the moduli spaces of parabolic symplectic orthogonal bundles on curves
[article]

2021
*
arXiv
*
pre-print

We prove that the moduli

arXiv:2101.02383v1
fatcat:5g232tuho5gcrm7qrzjqzdxbn4
*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. ...##
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Hard and soft edge spacing distributions for random matrix ensembles with orthogonal and symplectic symmetry
[article]

2006
*
arXiv
*
pre-print

at the hard and soft spectrum edges in the cases of

arXiv:math-ph/0605022v1
fatcat:4m2w7gywvnclxkrayxt72a4u4e
*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. ...##
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A stratification on the moduli spaces of symplectic and orthogonal bundles over a curve
[article]

2012
*
arXiv
*
pre-print

This invariant t defines stratifications on moduli

arXiv:1204.0834v1
fatcat:e2rip3roufgc3fdzaqofcl4crm
*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. ...##
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Moduli spaces of orthogonal and symplectic bundles over an algebraic curve

2008
*
Compositio Mathematica
*

of

doi:10.1112/s0010437x07003247
fatcat:4hthanjsnvebtfsphwva2b4nju
*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). ...##
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Partial ovoids and partial spreads in symplectic and orthogonal polar spaces

2008
*
European journal of combinatorics (Print)
*

sizes of large maximal partial ovoids and large maximal partial spreads in the classical

doi:10.1016/j.ejc.2007.06.004
fatcat:xcgvvewf3zhpzbmerhxtqzyrce
*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. ...##
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A stratification on the moduli spaces of symplectic and orthogonal bundles over a curve

2014
*
International Journal of Mathematics
*

This invariant t defines stratifications on moduli

doi:10.1142/s0129167x14500475
fatcat:6e3buai4sfhbxkamscxllqaify
*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. ...##
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Cyclic elliptic spreads
[article]

2015
*
arXiv
*
pre-print

In characteristic 2, an

arXiv:1512.00861v1
fatcat:zpxclaitsrc2phso5ggt4jinpy
*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*...##
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The symplectiness of Maxwell's equations

2008
*
2008 International Conference on Microwave and Millimeter Wave Technology
*

First, we analyze the continuoustime Maxwell's differential equations in free

doi:10.1109/icmmt.2008.4540337
fatcat:msppmodlzbdvjmzwdyowvevtli
*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*. ...##
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Teichmüller space for hyperkähler and symplectic structures

2015
*
Journal of Geometry and Physics
*

The quotient S/_0 is called the Teichmuller

doi:10.1016/j.geomphys.2015.07.006
fatcat:befuj4zow5hexlgndylztas75e
*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] . ...##
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Products of two involutions in classical groups of characteristic 2

1981
*
Journal of Algebra
*

Let k be a field of characteristic 2 and let V be a k-vector

doi:10.1016/0021-8693(81)90198-8
fatcat:czc3ahet2jghvots5s7f2gafhu
*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). ...
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