Related papers: SU(3) Clebsch-Gordan coefficients at large $N_c$

We have computed the Clebsch-Gordan coefficients for the product (000001) $\otimes$ (000001), where (000001) is the adjoint 78-dimensional representation of $E_6$. The results are presented for the dominant weights of the irreducible…

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…

We derive new explicit results for the Hilbert series of N=1 supersymmetric QCD with U(N_c) and SU(N_c) color symmetry. We use two methods which have previously been applied to similar computational problems in the analysis of decay of…

A family of infinite-dimensional irreducible $*$-representations on $\mathcal{H}\simeq L^2(\mathbb{R})\otimes\mathbb{C}^N$ is defined for a quantum-deformed Lorentz algebra $\mathscr{U}_{\bf q}(sl_2)\otimes \mathscr{U}_{\widetilde{\bf…

If R, S, T are irreducible SL_3-representations, we give an easy and explicit description of a basis of the space of equivariant maps from R tensor S to T. We apply this method to the rationality problem for invariant function fields. In…

The two parameters quantum algebra $SU_{p,k}(2)$ can be obtained from a single parameter algebra $SU_q(2)$. This fact gives some relations between $SU_{p,k}(2)$ quantities and the corresponding ones of the $SU_q(2)$ algebra. In this paper…

We present rules for rewriting SO(10) tensor and spinor invariants in terms of invariants of its ``Pati-Salam'' maximal subgroup (SU(4)$\times \rm{SU(2)}_L\times \rm{SU(2)}_R)$ supplemented by the discrete symmetry called D parity. Explicit…

We describe a framework for the controllability analysis of networks of $n$ quantum systems of an arbitrary dimension $d$, {\it qudits}, with dynamics determined by Hamiltonians that are invariant under the permutation group $S_n$. Because…

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain determinant representations for form factors of diagonal entries of the monodromy matrix. This representation can be used for the calculation of…

Motivated by the study of symmetries of C*-algebras, as well as by multivariate operator theory, we introduce the notion of an SU(2)-equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz-Pimsner…

Given a semisimple compact Lie group $G$ and a nonzero dominant integral weight $\lambda$, the highest weight $G_q$-modules $V_{n\lambda}$ form a subproduct system of finite dimensional Hilbert spaces. Using a conjectural asymptotic…

We determine spectral measures for some nimrep graphs arising in subfactor theory, particularly those associated with SU(3) modular invariants and subgroups of SU(3). Our methods also give an alternative approach to deriving the results of…

These are notes for the Aisenstadt lectures given in may/june 2002 at CRM, Montreal, enlarged and updated in 2014 by taking into account the recent results of Elias and Williamson on Soergel bimodules. The main object is the study of…

The microscopic justification of the emergence of SU(3) symmetry in heavy nuclei remains an interesting problem. In the past, the pseudo-SU(3) approach has been used, with considerable success. Recent results seem to suggest that the key…

We study two different SU(2) gauge-scalar theories in 3 and 4 spacetime dimensions. Firstly, we focus on the 3 dimensional SU(2) theory with multiple Higgs fields in the adjoint representation, that can be mapped to cuprate systems in…

Let H_c be the rational Cherednik algebra of type A_{n-1} with spherical subalgebra U_c = eH_ce. Then U_c is filtered by order of differential operators, with associated graded ring gr U_c = C[h+h*]^W, where W is the n-th symmetric group.…

The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a…

We derive the recurrence relation of irreducible tensor operator for O(4) in using the Wigner-Eckart theorem. The physical process like radiative transitions in atomic physics, nuclear transitions between excited nuclear states can be…

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the level of…

This is basically a summary of [Mu]. The focus of the paper is the explicit computation of Hecke operators for period functions. In particular we compute the matrix representations of the 2nd Hecke operator on period functions for the full…