相关论文: Permutation Group Symmetry and Correlations
Factors $\frac{X}{Y}$ in a free group $F$ with $Y$ normal in $X$ are considered. Precise results on the free structure of ${Y}$ relative to the free structure of ${X}$ when $\frac{X}{Y}$ is abelian are obtained. Some extensions and…
State symmetries are defined as permutations which act on vector spaces of column vectors and square matrices, resulting in isotropy groups for specific vector spaces. A large number of properties for such objects is shown, to provide a…
The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$,…
Four-dimensional N-extended superconformal symmetry and correlation functions of quasi-primary superfields are studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms…
We give a detailed analysis of the proportion of elements in the symmetric group on $n$ points whose order divides $m$, for $n$ sufficiently large and $m \ge n$ with $m = O(n)$.
Flavour symmetries are fundamental tools in the search for an explanation to the flavour puzzle: fermion mass hierarchies, the neutrino mass ordering, the differences between the mixing matrices in the quark and lepton sector, can all find…
Symmetric product orbifolds, i.e. permutation orbifolds of the full symmetric group S_{n} are considered by applying the general techniques of permutation orbifolds. Generating functions for various quantities, e.g. the torus partition…
We show that certain factor rings of the group algebra of a symmetric group have natural bases of group elements. We also give generators for the annihilator of certain permutation modules for symmetric groups.
We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing $F$-matrices (or the so-called $F$-basis) play an important…
Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on $d$ elements as a square $d\times d$ matrix. Motivated by [4], we define a similar class of matrices which are a generalization of…
Quark-lepton symmetric models are a class of gauge theories motivated by the similarities between the quarks and leptons. In these models the gauge group of the standard model is extended to include a ``color'' group for the leptons.…
The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm…
Symmetry plays a fundamental role in design of experiments. In particular, symmetries of factorial designs that preserve their statistical properties are exploited to find designs with the best statistical properties. By using a result…
The QCD-like gauge theory with adjoint fermions is considered in the field correlator formalism and the total spectrum of mesons and glueballs is obtained in agreement with available lattice data. A new state of a white fermion appears, as…
We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals.
$\mu$-$\tau$ symmetry imposed on the neutrino mass matrix in the flavour basis is known to be quite predictive. We integrate this very specific neutrino symmetry into a more general framework based on the supersymmetric SO(10) grand unified…
This paper is concentrated on the classification of permutation matrix with the permutation similarity relation, mainly about the canonical form of a permutational similar equivalence class, the cycle matrix decomposition of a permutation…
We derive exact relations between the Renyi entanglement entropies and the particle number fluctuations of spatial connected regions in systems of N noninteracting fermions in arbitrary dimension. We prove that the asymptotic large-N…
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
Unification based on the group SO(10)^3 \times S_3 is studied. Each family has its own SO(10) group, and the S_3 permutes the three families and SO(10) factors. This is the maximal local symmetry for the known fermions. Family unification…