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On the Universal Embedding of the U2n(2) Dual Polar Space

Paul Li
2002 Journal of combinatorial theory. Series A  
Brouwer has shown that the universal embedding of the U 2n (2) dual polar space has dimension at least (4 n +2)/3 and has conjectured equality.  ...  The method is the same used in the author's previous paper on an analogous question for the Sp 2n (2) dual polar space. © 2002 Elsevier Science (USA)  ...  Another motivation for studying the embeddings of DU 2n (2) comes from Ivanov's work on extended dual polar spaces [5] .  ... 
doi:10.1006/jcta.2001.3211 fatcat:72bbjivypfbwndb2hbo2wtt5nm

A note on embedding and generating dual polar spaces

B. N. Cooperstein, E. E. Shult
2001 Advances in Geometry  
A survey is included summarizing current knowledge of the generating rank and universal embedding spaces of dual polar spaces.  ...  Generating sets of cardinality 2 n are constructed for the unitary dual polar space DU2n 1Y q 2 and the elliptic orthogonal dual polar space DO À 2n 2Y q.  ...  The polar space and dual polar spaces of type UkY q 2 .  ... 
doi:10.1515/advg.2001.003 fatcat:qunqogdjyzdxvnkoeorzuuhw44

On the Jacobian of hyperelliptic curves y^2 = x^5 + m^2 [article]

Keunyoung Jeong, Junyeong Park, Donggeon Yhee
2021 arXiv   pre-print
In this paper, we study the algebraic rank and the analytic rank of the Jacobian of hyperelliptic curves y^2 = x^5 + m^2 for integers m.  ...  Namely, we first provide a condition on m that gives a bound of the size of Selmer group and then we provide a condition on m that makes L-functions non-vanishing.  ...  Let λ : J → Jb be the canonical polarization of J and let φb be the dual isogeny of φ. Let Ψ := b ⊂ J[q] and choose a GK -invariant set of divisor classes that generate Ψ.  ... 
arXiv:2104.03156v2 fatcat:pj24zem7t5fshc3jlq3wiz4mbm

Flag-homogeneous compact connected polygons

T. Grundhöfer, N. Knarr, L. Kramer
1995 Geometriae Dedicata  
The flag-homogeneous compact connected polygons with equal topological parameters p = q are classified explicitly. These polygons turn out to be Moufang polygons.  ...  Acknowledgements The authors would like to thank Richard BOdi and Hermann H~ihl for various helpful discussions, and Markus Stroppel for important remarks concerning the proof of 3.7.  ...  By the result of Dienst [9] on quadrangles embedded into projective spaces, ~ is the real symplectic quadrangle. [] 3.5 THEOREM.  ... 
doi:10.1007/bf02179088 fatcat:hdzmtrvm2naqbabnbl7kq4nzx4

SU-bordism: structure results and geometric representatives [article]

Georgy Chernykh, Ivan Limonchenko, Taras Panov
2019 arXiv   pre-print
In the first part of this survey we give a modernised exposition of the structure of the special unitary bordism ring, by combining the classical geometric methods of Conner-Floyd, Wall and Stong with  ...  the Adams-Novikov spectral sequence and formal group law techniques that emerged after the fundamental 1967 work of Novikov.  ...  The homotopic approach is based on the notion of the MSU -spectrum. Let η n denote the universal (tautological) complex n-plane bundle over BSU (n). The Thom space of η n is denoted by MSU (n).  ... 
arXiv:1903.07178v2 fatcat:6cbgws42p5eyvkh733mziz2xqe

A theory of characteristic currents\\ associated with a singular connection

Reese Harvey, H. Blaine Lawson Jr.
1994 Bulletin of the American Mathematical Society  
They would especially like to thank John Zweck who carefully read the manu script and made a number of important suggestions and comments. The authors would also like to thank Mrs.  ...  The authors would like to thank Bill Fulton for some very useful remarks.  ...  dual coordinates on (C 71 )*.  ... 
doi:10.1090/s0273-0979-1994-00497-5 fatcat:nxazjoezq5fatncxqbdkhruojq

Multi-instanton calculus and the AdS/CFT correspondence in superconformal field theory

Nicholas Dorey, Timothy J. Hollowood, Valentin V. Khoze, Michael P. Mattis, Stefan Vandoren
1999 Nuclear Physics B  
We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of a single copy of AdS_5 x S^5. (2) The integration measure on this space  ...  with Type IIB string calculations, at the k-instanton level, G_n = √(N) g^8 k^n-7/2 e^2π ikτ∑_d|k d^-2 F_n(x_1,...  ...  (2.23) It follows that the physical moduli space, Mkphys , of inequivalent self-dual gauge configurations in the topological sector k is the quotient of the space Mk of all solutions of the ADHM  ... 
doi:10.1016/s0550-3213(99)00193-5 fatcat:2klaxkzr6vbe7cbdmrppwuew5u

Fourier-Jacobi models of Deligne-Lusztig characters and depth zero local descent for unitary groups [article]

Dongwen Liu, Jia-Jun Ma, Fang Shi
2022 arXiv   pre-print
The result is a concrete example in the context of non-tempered Gan-Gross-Prasad program.  ...  In this paper, we deduce explicit multiplicity formulas of the Fourier-Jacobi model for Deligne-Lusztig characters of finite symplectic groups, unitary groups, and general linear groups.  ...  Let V be a symplectic f-space of dimension 2n defined over f, on which G acts by symplectic automorphisms, such that we have an embedding G ãÑ SppV q. Fix a nontrivial additive character ψ of f.  ... 
arXiv:2208.02308v1 fatcat:xop3yxbbx5bsjldy4qcpk7bsiu

Non-Abelian Representations of Geometries

A. A. Ivanov
Groups and Combinatorics: In memory of Michio Suzuki   unpublished
Let g be a geometry in which the elements of one type are called points and the elements of some other type are called lines.  ...  of 1/J and whenever {xoo, xo, ... , Xp-1} is the set of points incident to a line, the subgroups 'lj;(xoo), '1/J(xo), ... , 1/J(xp-1) are pairwise different and generate in R a subgroup of order p 2 •  ...  Similarly representations of the dual polar spaces with 3 points on a line (associated with Sp2n(2) and U2n(2)) give their c-extensions.  ... 
doi:10.2969/aspm/03210301 fatcat:7gmu23m5gnbxldxlzselg2j3vy

Time reversal symmetry and the geometric phase [article]

Mattias Torbjörn Johnsson, University Of Canterbury
With this background, and using a definition of time reversal symmetry based on the evolution operator, I demonstrate that the existence of a non-zero geometric phase can in all cases be attributed to  ...  Furthermore, following a conformal transformation these potentials can be mapped to those of the SU(2) instanton/anti-instanton pair.  ...  For example if the embedding space is two dimensional and the subspace is a zero-dimensional point, loops can be defined, as they can in the case of a line in the three dimensional space.  ... 
doi:10.26021/7323 fatcat:3z2ccqelozcqfbswsxtzm7aed4

A study of quantum circuits based on semiconductor structures

Κωνστνατίνος Ε. Προύσαλης
The problem of quantum computation is studied via the quantum circuit model, when this type of computation is conducted on semiconductor technologies.  ...  Due to the need for larger fault tolerant quantum computing systems, this study focuses more on the major problem of quantum noise.  ...  In Fig. 2, a standard universal set of gates [2] is presented with its established notations.  ... 
doi:10.26262/ fatcat:ppzjimfmyrfe3gftqgzgja4r5i