Search results for "Mathematical physics"
showing 10 items of 2687 documents
On the Oort conjecture for Shimura varieties of unitary and orthogonal types
2014
In this paper we study the Oort conjecture on Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety $\mathcal{A}_g$. Using the poly-stability of Higgs bundles on curves and the slope inequality of Xiao on fibred surfaces, we show that a Shimura curve $C$ is not contained generically in the Torelli locus if its canonical Higgs bundles contains a unitary Higgs subbundle of rank at least $(4g+2)/5$. From this we prove that a Shimura subvariety of $\mathbf{SU}(n,1)$-type is not contained generically in the Torelli locus when a numerical inequality holds, which involves the genus $g$, the dimension $n+1$, the degree $2d$ of CM field of the Hermitian space,…
THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA osp(1, 2n)
2006
http://www.worldscinet.com/jaa/05/0503/S0219498806001740.html; International audience; Based on Kostant's cohomological interpretation of the Amitsur–Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras osp(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur–Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated.
Geometry and arithmetic of Maschke's Calabi-Yau three-fold
2011
Maschke's Calabi-Yau three-fold is the double cover of projective three space branched along Maschke's octic surface. This surface is defined by the lowest degree invariant of a certain finite group acting on a four-dimensional (4D) vector space. Using this group, we show that the middle Betti cohomology group of the three-fold decomposes into the direct sum of 150 2D Hodge substructures. We exhibit 1D families of rational curves on the three-fold and verify that the associated Abel-Jacobi map is non-trivial. By counting the number of points over finite fields, we determine the rank of the Neron-Severi group of Maschke's surface and the Galois representation on the transcendental lattice of…
Invariant Markov semigroups on quantum homogeneous spaces
2019
Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coideal *-subalgebras. Several one-to-one correspondences between such invariant functionals are established. Adding a positivity condition, this yields one-to-one correspondences of invariant quantum Markov semigroups acting on expected coideal *-subalgebras and certain convolution semigroups of states on the underlying compact quantum group. This gives an approach to classifying invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators …
Picard-Fuchs operators for octic arrangements, I: the case of orphans
2019
We report on $25$ families of projective Calabi-Yau threefolds that do not have a point of maximal unipotent monodromy in their moduli space. The construction is based on an analysis of certain pencils of octic arrangements that were found by C. Meyer. There are seven cases where the Picard-Fuchs operator is of order two and $18$ cases where it is of order four. The birational nature of the Picard-Fuchs operator can be used effectively to distinguish between families whose members have the same Hodge numbers.
Local Spectral Theory for R and S Satisfying RnSRn = Rj
2020
In this paper, we analyze local spectral properties of operators R,S and RS which satisfy the operator equations RnSRn=Rj and SnRSn=Sj for same integers j&ge
Algebraische Approximationen hoher Ordnung an die Exponentialfunktion
1992
Im Zusammenhang mit der numerischen Behandlung von Anfangswertproblemen bei gewohnlichen Differentialgleichungen fuhrt der Begriff der absoluten Stabilitat bei sogenannten einwertigen Verfahren auf gewisse rationale Approximationen der Exponentialfunktion, wie z. B. Pade-Approximationen. Aus der Untersuchung dieser rationalen Approximationen haben sich verschiedene Theorien entwickelt, als Beispiel sei die Theorie der Ordnungssterne von Wanner, Hairer und Norsett genannt. Im selben Zusammenhang ergeben sich bei der Anwendung von mehrwertigen Verfahren algebraische Approximationen der Exponentialfunktion. In der vorliegenden Arbeit wird fur Butchers verallgemeinerte implizite Runge-Kutta Met…
Relations between natural and observable measures
2005
We give a complete description of relations between observable and natural measures in connection with invariance, ergodicity and absolute continuity.
Noncancellation for contractible affine threefolds
2011
We construct two nonisomorphic contractible affine threefolds X X and Y Y with the property that their cylinders X × A 1 X\times \mathbb {A}^{1} and Y × A 1 Y\times \mathbb {A}^{1} are isomorphic, showing that the generalized Cancellation Problem has a negative answer in general for contractible affine threefolds. We also establish that X X and Y Y are actually biholomorphic as complex analytic varieties, providing the first example of a pair of biholomorphic but not isomorphic exotic A 3 \mathbb {A}^{3} ’s.
Finite Groups with Odd Sylow Normalizers
2016
We determine the non-abelian composition factors of the finite groups with Sylow normalizers of odd order. As a consequence, among others, we prove the McKay conjecture and the Alperin weight conjecture for these groups.