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61.
We characterize the finite Veronesean
of all Hermitian varieties of PG(n,q2) as the unique representation of PG(n,q2) in PG(d,q), d n(n+2), where points and lines of PG(n,q2) are represented by points and ovoids of solids, respectively, of PG(d,q), with the only condition that the point set of PG(d,q) corresponding to the point set of PG(n,q2) generates PG(d,q). Using this result for n=2, we show that
is characterized by the following properties: (1)
; (2) each hyperplane of PG(8,q) meets
in q2+1, q3+1 or q3+q2+1 points; (3) each solid of PG(8,q) having at least q+3 points in common with
shares exactly q2+1 points with it.51E24 相似文献
62.
This is a first step toward the determination of the parameters of two-point codes on a Hermitian curve. We describe the dimension of such codes and determine the minimum distance of some two-point codes.AMS Classification: 94B27, 14H50, 11T71, 11G20Masaaki Homma - Partially supported by Grant-in-Aid for Scientific Research (15500017), JSPS.Seon Jeong Kim - Partially supported by Korea Research Foundation Grant (KRF-2002-041-C00010). 相似文献
63.
Hennie De Schepper Alí Guzmán Adán Frank Sommen 《Journal of Mathematical Analysis and Applications》2018,457(1):23-50
In [4] we studied the group invariance of the inner product of supervectors as introduced in the framework of Clifford analysis in superspace. The fundamental group leaving invariant such an inner product turns out to be an extension of and gives rise to the definition of the spin group in superspace through the exponential of the so-called extended superbivectors, where the spin group can be seen as a double covering of by means of the representation . In the present paper, we study the invariance of the Dirac operator in superspace under the classical H and L actions of the spin group on superfunctions. In addition, we consider the Hermitian Clifford setting in superspace, where we study the group invariance of the Hermitian inner product of supervectors introduced in [3]. The group of complex supermatrices leaving this inner product invariant constitutes an extension of and is isomorphic to the subset of of elements that commute with the complex structure J. The realization of within the spin group is studied together with the invariance under its actions of the super Hermitian Dirac system. It is interesting to note that the spin element leading to the complex structure can be expressed in terms of the n-dimensional Fourier transform. 相似文献
64.
In this paper we study a key example of a Hermitian symmetric space and a natural associated double flag variety, namely for the real symplectic group G and the symmetric subgroup L, the Levi part of the Siegel parabolic . We give a detailed treatment of the case of the maximal parabolic subgroups Q of L corresponding to Grassmannians and the product variety of and ; in particular we classify the L-orbits here, and find natural explicit integral transforms between degenerate principal series of L and G. 相似文献
65.
Maria Montanucci 《代数通讯》2018,46(11):4739-4776
66.
In this paper, by employing some results on Kummer extensions, we give an arithmetic characterization of pure Weierstrass gaps at many totally ramified places on a quotient of the Hermitian curve, including the well-studied Hermitian curve as a special case. The cardinality of these pure gaps is explicitly investigated. In particular, the numbers of gaps and pure gaps at a pair of distinct places are determined precisely, which can be regarded as an extension of the previous work by Matthews (2001) considered Hermitian curves. Additionally, some concrete examples are provided to illustrate our results. 相似文献
67.
Given a Hermitian manifold(M~n, g), the Gauduchon connections are the one parameter family of Hermitian connections joining the Chern connection and the Bismut connection. We will call▽~s=(1-s/2)▽~c+s/2▽~b the s-Gauduchon connection of M, where ▽~c and ▽~b are respectively the Chern and Bismut connections. It is natural to ask when a compact Hermitian manifold could admit a flat s-Gauduchon connection. This is related to a question asked by Yau. The cases with s = 0(a flat Chern connection) or s = 2(a flat Bismut connection) are classified respectively by Boothby in the1950 s or by the authors in a recent joint work with Q. Wang. In this article, we observe that if either s ≥ 4 + 2×3~(1/2) ≈ 7.46 or s ≤ 4-2×3~(1/2) ≈ 0.54 and s ≠ 0, then g is K?hler. We also show that, when n = 2,g is always K?hler unless s = 2. Therefore non-K?hler compact Gauduchon flat surfaces are exactly isosceles Hopf surfaces. 相似文献
68.
We introduce two new linear differential operators which are invariant with respect to the unitary group SU(n). They constitute analogues of the twistor and the Rarita-Schwinger operator in the orthogonal case. The natural setting for doing this is Hermitian Clifford Analysis. Such operators are constructed by twisting the two versions of the Hermitian Dirac operator 6z_ and 6z_ and then projecting on irreducible modules for the unitary group. We then study some properties of their spaces of nullsolutions and we find a formulation of the Hermitian Rarita-Schwinger operators in terms of Hermitian monogenic polynomials. 相似文献
69.
70.
Ai-Li Yang 《Applied mathematics and computation》2010,216(6):1715-1722
Based on the HSS (Hermitian and skew-Hermitian splitting) and preconditioned HSS methods, we will present a generalized preconditioned HSS method for the large sparse non-Hermitian positive definite linear system. Our method is essentially a two-parameter iteration which can extend the possibility to optimize the iterative process. The iterative sequence produced by our generalized preconditioned HSS method can be proven to be convergent to the unique solution of the linear system. An exact parameter region of convergence for the method is strictly proved. A minimum value for the upper bound of the iterative spectrum is derived, which is relevant to the eigensystem of the products formed by inverse preconditioner and splitting. An efficient preconditioner based on incremental unknowns is presented for the actual implementation of the new method. The optimality and efficiency are effectively testified by some comparisons with numerical results. 相似文献