The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to q = 4 and exhibits duality and integrability away from critical temperature in absence of magnetic field. We show how, when a magnetic field is switched on, it provides the simplest model of confinement allowing for...

We prove potential automorphy results for a single Galois representation $$G_F\rightarrow GL_n(\overline{\mathbb {Q}}_l)$$ where F is CM number field. The strategy to use the p, q switch trick go between p-adic and q-adic realisation of certain variant Dwork motive. choose this break self-duality shape motives, but not Hodge-Tate weights. Another key result that representations we come from mot...

Necessary conditions for Pareto optimality in multiobjective programming with subdifferentiable set functions are established in Theorem 12 of H. C. Lai and L. J. Ž . Lin J. Math. Anal. Appl. 132, 1988, 558]571 . In this paper, we establish some sufficient conditions under which a feasible solution of such a problem will be Pareto optimal provided that a weaker convexity requirement is satisfie...

A large fraction of the world data on both polarized and unpolarized inclusive ep scattering at large Bjorken x lies in the resonance region where a correspondence with the deep inelastic regime, known as Bloom and Gilman’s duality, was observed. Recent analyses of the Q dependence of the data show that partonhadron duality is inconsistent with the twist expansion at low values of the final sta...

Motivated by recent developments on calculus in metric measure spaces (X, d,m), we prove a general duality principle between Fuglede’s notion [15] of p-modulus for families of finite Borel measures in (X, d) and probability measures with barycenter in Lq(X,m), with q dual exponent of p ∈ (1,∞). We apply this general duality principle to study null sets for families of parametric and non-paramet...

We investigate the homology of a congruence subgroup Γ SL3(Z) with coefficients in Steinberg modules St(Q3) and St(E3), where E is real quadratic field are Q. By Borel-Serre duality, H0(Γ,St(Q3)) isomorphic to H3(Γ,Q). Taking image connecting homomorphism H1(Γ,St(E3)/St(Q3))→H0(Γ,St(Q3)), followed by isomorphism, we obtain naturally defined Hecke-stable subspace H(Γ,E) conjecture that independe...

Various aspects of multihadron production can be revealed through multiplicity fluctuations and particle correlations studies. The fluctuations are sensitive to soft particle dynamics and their measurements allow to test perturbative QCD 1 and local parton hadron duality (LPHD) hypothesis . In BEC studies , the correlation function gives information about the shape, size and lifetime of the bos...

The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to q = 4 and exhibits duality and integrability away from critical temperature in absence of magnetic field. We show how, when a magnetic field is switched on, it provides the simplest model of confinement allowing for...

The braided approach to q-deformation (due to the author and collaborators) gives natural algebras R21u1Ru2 = u2R21u1R and R21x1x2 = x2x1R for q-Minkowski and q-Euclidean spaces respectively. These algebras are covariant under a corresponding background ‘rotation’ quantum group. Semidirect product by this according to the bosonisation procedure (also due to the author) gives the corresponding P...

We study the N = 2 coset models in their formulation as supersymmetric gauged Wess-Zumino-Witten models. A model based on the coset G/H is invariant under a symmetry group isomorphic to ZZk+Q, where k is the level of the model and Q is the dual Address after September 1, 1994: Department of Physics, Yale University, New Haven, CT 06511 Coxeter number of G. Using a duality-like relationship, we ...