421 research outputs found
Pfaffians and Representations of the Symmetric Group
Pfaffians of matrices with entries z[i,j]/(x\_i+x\_j), or determinants of
matrices with entries z[i,j]/(x\_i-x\_j), where the antisymmetrical
indeterminates z[i,j] satisfy the Pl\"ucker relations, can be identified with a
trace in an irreducible representation of a product of two symmetric groups.
Using Young's orthogonal bases, one can write explicit expressions of such
Pfaffians and determinants, and recover in particular the evaluation of
Pfaffians which appeared in the recent literature.Comment: 28
Methods for multiloop calculations and Higgs boson production at the LHC
The main topics of this thesis are Higgs boson production and the program package TopoID. We calculated results for all collinear counterterms up to N3LO. For a particular class of triple-real integrals we obtained results with full dependence on x. TopoID is designed to be a process independent tool for topology identification, FORM code generation and finding non-trivial relations among integrals that remain after applying a reduction algorithm
The Shimura-Taniyama Conjecture and Conformal Field Theory
The Shimura-Taniyama conjecture states that the Mellin transform of the
Hasse-Weil L-function of any elliptic curve defined over the rational numbers
is a modular form. Recent work of Wiles, Taylor-Wiles and
Breuil-Conrad-Diamond-Taylor has provided a proof of this longstanding
conjecture. Elliptic curves provide the simplest framework for a class of
Calabi-Yau manifolds which have been conjectured to be exactly solvable. It is
shown that the Hasse-Weil modular form determined by the arithmetic structure
of the Fermat type elliptic curve is related in a natural way to a modular form
arising from the character of a conformal field theory derived from an affine
Kac-Moody algebra
GEOTHER 1.1: Handling and Proving Geometric Theorems Automatically
Colloque avec actes et comité de lecture. internationale.International audienceGEOTHER provides an environment for handling and proving theorems in geometry automatically. In this environment, geometric theorems are represented by means of predicate specifications. Several functions are implemented that allow one to translate the specification of a geometric theorem into English and Chinese statements, into algebraic expressions, and into logic formulas automatically. Geometric diagrams can also be drawn automatically from the predicate specification, and the drawn diagrams may be modified and animated with mouse click and dragging. Five algebraic provers based on Wu's method of characteristic sets, the Gröbner basis method, and other triangularization techniques are available for proving such theorems in elementary (and differential) geometry. Geometric meanings of the produced algebraic nondegeneracy conditions can be interpreted automatically, in most cases. PostScript and HTML files can be generated, also automatically, to document the manipulation and machine proof of the theorem. This paper presents these capabilities of GEOTHER, addresses some implementation issues, and reports on the performance of GEOTHER's algebraic provers
New candidates for multivariate trapdoor functions
We present a new method for building pairs of HFE polynomials of high degree, such that the map constructed with such a pair is easy to invert. The inversion is accomplished using a low degree polynomial of Hamming weight three, which is derived from a special reduction via Hamming weight three polynomials produced by these two HFE polynomials. This allows us to build new candidates for multivariate trapdoor functions in which we use the pair of HFE polynomials to fabricate the core map. We performed the security analysis for the case where the base field is and showed that these new trapdoor functions have high degrees of regularity, and therefore they are secure against the direct algebraic attack. We also give theoretical arguments to show that these new trapdoor functions over are secure against the MinRank attack as well
- …