Related papers: A note on the four-dimensional Kirby calculus
A new link between tetrahedra and the group SU(2) is pointed out: by associating to each face of a tetrahedron an irreducible unitary SU(2) representation and by imposing that the faces close, the concept of quantum tetrahedron is seen to…
A general group element for the fundamental representation of SU(3) is expressed as a second order polynomial in the hermitian generating matrix H, with coefficients consisting of elementary trigonometric functions dependent on the sole…
This is an expository account of the author's collaboration with Rob Kirby leading up to the theory of trisections of smooth 4-manifolds. This article was written for inclusion in an upcoming issue of Celebratio Mathematica dedicated to Rob…
By representing the electroweak gauge symmetry group $SU(2) \times U(1)$ by a hypertorus $S_2 \times S_1$, the electroweak mixing angle and the fine structure constant are predicted. By representing neutrinos as oscillating spheroid…
We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor…
Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given…
The matrix elements connected non physic angles space representation with the space of physic observables of alternative O(2,4) world found on explicit form. All such matrix elements are represented in terms of solutions of Gauss…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We introduce a unified framework for counting representations of knot groups into $SU(2)$ and $SL(2, \mathbb{R})$. For a knot $K$ in the 3-sphere, Lin and others showed that a Casson-style count of $SU(2)$ representations with fixed…
The full spatial distribution of the color fields of two and four static quarks is measured in lattice SU(2) field theory at separations up to 1 fm at beta=2.4. The four-quark case is equivalent to a qbar q qbar q system in SU(2) and is…
Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way,…
We apply the theory of branches in Bruhat-Tits trees, developed in previous works by the second author and others, to the study of two dimensional representations of finite groups over the ring of integers of a number field. We provide a…
We develop an abstract framework for the investigation of quantization and dequantization procedures based on orthogonality relations that do not necessarily involve group representations. To illustrate the usefulness of our abstract method…
We investigate supersymmetric $SU(4)_c\times SU(4)_{L+R}$ theory in 5 dimensions whose compactification on a $S^{(1)}/Z_2$ orbifold yields N=1 supersymmetric $SU(4)_c\times SU(2)_L\times SU(2)_R$ supplemented by a $\tl{U}(1)$ gauge…
A four dimensional non-trivial extension of the Poincar\'e algebra different from supersymmetry is explicitly studied. Representation theory is investigated and an invariant Lagrangian is exhibited. Some discussion on the Noether theorem is…
Algebraic structure of a class of differential equations including Heun is shown to be related with the deformations of sl(2) algebra. These include both quadratic and cubic ones. The finite dimensional representation of cubic algebra is…
The SU(3) irreducible representations (irreps) are characterised by the (lambda, mu) Elliott quantum numbers, which are necessary for the extraction of the nuclear deformation, the energy spectrum and the transition probabilities. These…
We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is…
The paper consists of two parts. The first part introduces the representation ring for the family of compact unitary groups U(1), U(2),.... This novel object is a commutative graded algebra R with infinite-dimensional homogeneous…
We study the existence of irreducible $SU(2)$-representations for cyclic branched covers of knots in $S^3$. Our main result establishes that if $K$ is a non-trivial prime knot and $d$ is an integer such that $d \geq 2$ and $\Sigma_d(K)$ is…