we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

We construct and analyze dual N = 4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters. We analyze the classical and the quantum moduli spaces of the theories and construc...

The tensor product of a positive and a negative discrete series representation of the quantum algebra Uq ( su(1, 1) ) decomposes as a direct integral over the principal unitary series representations. Discrete terms can appear, and these terms are a finite number of discrete series representations, or one complementary series representation. From the interpretation as overlap coefficients of li...

We determine all D-branes in the non-tachyonic 0’B orientifold, examine their world-volume anomalies and study orbifold compactifications. We find that the spectrum of the D-branes contains chiral fermions in the symmetric, antisymmetric and fundamental representations of (unitary) gauge groups on the branes. The cancellation of the world-volume anomalies requires Wess-Zumino terms which we det...

A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of are perturbable to genuine in point-norm topology. For large classes groups G, we show that matricial stability implies vanishing rational cohomology all nonzero even dimensions. We revisit a method constructing almost flat K-theory BG which involves dual assembly map and quasidia...

| The Gabor transform yields a discrete representation of a signal in the phase space 1, 2]. Since the Gabor transform is non-orthogonal, eecient reconstruction of a signal from its phase space samples is not straightforward and involves the computation of the so-called dual Gabor function. We present a unifying approach to the derivation of numerical algorithms for discrete Gabor analysis, bas...

It is shown that, for both compact and non-compact Lie groups, vector-coherent-state methods provide straightforward derivations of holomorphic representations on symmetric spaces. Complementary vector-coherent-state methods are introduced to derive pairs of holomorphic representations which are bi-orthogonal duals of each other with respect to a simple Bargmann inner product. It is then shown ...

In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki ${U}_{\mathrm{KT}}$, which defines duality between Haldane phase and ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry-breaking phase. this paper, we find that ${U}_{\mathrm{KT}}$ also topological Ising critical trivial phase, provides ``hidden symmetry breaking'' interpr...

We twist the monopole equations of Seiberg and Witten and show how these equations are realized in topological Yang-Mills theory. A Floer derivative and a Morse functional are found and are used to construct a unitary transformation between the usual Floer cohomologies and those of the monopole equations. Furthermore, these equations are seen to reside in the vanishing self-dual curvature condi...

Complex Ginzburg-Landau Equations were originated in the theory of Super-conductivity, 13]. When Ginzburg-Landau parameter chosen to be a special constant, the equations are called self-dual vortex equations that were carefully studied by Jaae and Taubes 16]. For the vortex equation on a Riemannian surface , one considers an open, smooth domain with, possibly empty, smooth boundary @. Let L be ...