Related papers: Self-conjugate representation SU(3) chains

We develop simple computational techniques for constructing all possible SU(3) representations in terms of irreducible SU(3) Schwinger bosons. We show that these irreducible Schwinger oscillators make SU(3) representation theory as simple…

Let $G$ be a finite group and let $p$ be a prime. In this paper, we study the structure of finite groups with a large number of $p$-regular conjugacy classes or, equivalently, a large number of irreducible $p$-modular representations. We…

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…

A contractive $n$-tuple $A=(A_1,...,A_n)$ has a minimal joint isometric dilation $S=(S_1,...,S_n)$ where the $S_i$'s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When $A$…

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…

We describe the geometry of the character variety of representations of the fundamental group of the complement of a Hopf link with $n$ twists, namely $\Gamma_{n}=\langle x,y \,| \, [x^n,y]=1 \rangle$ into the group $\mathrm{SU}(r)$. For…

Models with spontaneously broken parity symmetry can solve the strong $CP$ problem in a natural way. We construct such a model in the context of $\SU3^3$ unification. Parity has the conventional meaning in this model, and the gauge group is…

We establish the spectral gap property for dense subgroups of $SU(d)$ ($d\geq 2$), generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof differs, in several crucial aspects, from…

We show that if $Y$ is a toroidal closed graph manifold rational homology $3$-sphere with $|H_1(Y;\mathbb{Z})| \le 5$, then there exists an irreducible representation $\fund{Y} \to SU(2)$, using topological methods and avoiding the use of…

A cuprate superconductor model based on the analogy with atomic nuclei was shown by Iachello to have an $su(3)$ structure. The mean-field approximation Hamiltonian can be written as a linear function of the generators of $su(3)$ algebra.…

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation…

Any stretching of Ringel's non-Pappus pseudoline arrangement when projected into the Euclidean plane, implicitly contains a particular arrangement of nine triangles. This arrangement has a complex constraint involving the sines of its…

Let $p<q$ be odd primes, $\rho_1$ and $\rho_2$ be irreducible representations of $\text{SL}(2,\mathbb{Z}_p)$ and $\text{SL}(2,\mathbb{Z}_q)$ of dimensions $\frac{p+1}{2}$ and $\frac{q+1}{2}$, respectively. We show that if…

We show that the knot group of any knot in any integer homology sphere admits a non-abelian representation into $SU(3)$ such that meridians are mapped to matrices whose eigenvalues are the three distinct third roots of unity. This answers…

In this paper we investigate the problem of spontaneous supersymmetry breaking without a cosmological term in $N=3$ supergravity with matter vector multiplets, scalar fields geometry being $SU(3,m)/SU(3)\otimes SU(m)\otimes U(1)$. At first,…

For any subfield K of the complex numbers which is not contained in an imaginary quadratic number field, we construct conjugate varieties whose algebras of K-rational (p,p)-classes are not isomorphic. This compares to the Hodge conjecture…

Motivated by the study of an Hecke action on iterated Shimura integrals undertaken in [H], in this appendix to [H] we prove that, for any prime $p \geq 5$ and for any integer $n \geq 1$, every complex irreducible representation of…

The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…

In this short note we show that every connected reductive simply-connected algebraic group of rank $>1$ over the complex numbers has infinitely many pairs of irreducible representations which are not related by an automorphism of the…

We propose a set of 4 recurrence relations whose linear combination gives the number of group invariants, equivalently the dimension of the invariant subspace, in the tensor product of an arbitrary number of adjoint representations of the…