Related papers: Formulas for SU(3) Matrices
We show that each irreducible tensor representation of weight 2 of the rotation group of three-dimensional space in the space of rank 3 covariant tensors gives rise to an associative algebra with unity. We find the algebraic relations that…
We construct a 3-3-1 model for three families that can be embedded into a single SU(8) unified model. Assuming appropriate branching rules and symmetry-breaking pattern, we find a complete fermion content within irreducible representations…
It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra $ M_{ q,p}(2) $ ( the coordinate ring of $ GL_{q,p}(2) $) exist only when both q and p are roots of unity. In this case th e space of states…
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…
A central question in Quantum Computing is how matrices in $SU(2)$ can be approximated by products over a small set of generators. A topology will be defined on $SU(2)$ so as to introduce the notion of a covering exponent which compares the…
A C-Language program which tabulates the isoscalar factors and Clebsch-Gordan coefficients for products of representations in SU(3) is presented. These are efficiently computed using recursion relations, and the results are presented in…
We consider decomposition of coordinate independent states into SO(9)xSU(2) representations in SU(2) Matrix theory. To see what and how many representations appear in the decomposition, we compute the character, which is given by a trace…
A closed and explicit formula for all $\su{(3)}_k$ fusion coefficients is presented which, in the limit $k \rightarrow \infty$, turns into a simple and compact expression for the $su(3)$ tensor product coefficients. The derivation is based…
We recall the classification of the irreducible representations of $SL(2)_q$, and then give fusion rules for these representations. We also consider the problem of $\cR$-matrices, intertwiners of the differently ordered tensor products of…
We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…
We examine what integers are representable as sums of three cubes. We also provide formulas for the number of representations of $x^3+y^3+z^3=n$ under the condition $x+y+z=t$. Also we show how the problem of three cubes is related to…
The reciprocal Pascal matrix has entries $\binom{i+j}{j}^{-1}$. Explicit formullae for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, $q$-analogues are also presented.
The $SU(2)$ unitary matrix $U$ employed in hadronic low-energy processes has both exponential and analytic representations, related by $ U = \exp\left[ i \mathbf{\tau} \cdot \hat{\mathbf{\pi}} \theta\,\right] = \cos\theta I + i…
In this article we give examples which show that the TQFT representations of the mapping class groups derived from quantum SU(N) for N>2 are generically decomposable. One general decomposition of the representations is induced by the…
Quantum computation started to become significant field of studies as it hold great promising towards the upgrade of our current computational power. Studying the evolution of quantum states serves as a good fundamental in understanding…
The SU$(1,1)$ group plays a fundamental role in various areas of physics, including quantum mechanics, quantum optics, and representation theory. In this work we revisit the holomorphic discrete series representations of SU$(1,1)$, with a…
The general expression for the local matrix $t(\theta)$ of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing $t(\theta)$ from the fundamental representation and imposing the…
We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a…
We present a new approach for the Talmi-Moshinsky transformation representation in the harmonic oscillator basis. We utilize the SU(3) scheme for the calculation of harmonic oscillator brackets. Using this scheme we obtain the explicit…
We present the exact solution of the Richardson-Gaudin models associated with the SU(3) Lie algebra. The derivation is based on a Gaudin algebra valid for any simple Lie algebra in the rational, trigonometric and hyperbolic cases. For the…