The p – q duality is a relation between the (p, q) model and the (q, p) model of two-dimensional quantum gravity. Geometrically this duality corresponds to a relation between the two relevant points of the Sato Grassmannian. Kharchev and Marshakov have expressed such a relation in terms of matrix integrals. Some explicit formulas for small p and q have been given in the work of Fukuma-Kawai-Nak...

We establish a new Howe duality between a pair of two queer Lie superalgebras (q(m), q(n)). This gives a representation theoretic interpretation of a well-known combinatorial identity for Schur Q-functions. We further establish the equivalence between this new Howe duality and the Schur–Sergeev duality between q(n) and a central extension H̃k of the hyperoctahedral group Hk. We show that the zer...

Degenerating the quantum queer Schur superalgebra ${\mathcal{Q}_q(n,r; R)}$ to case $q=1$, ${\mathcal{Q}(n,r)}$ is obtained. In this article, we reconstruct universal enveloping algebra ${U({\mathfrak{q}_n})}$ of Lie ${\mathfrak{q}_n}$ via ${\mathcal{Q}(n,r)}$, and achieve another explanation Schur-Weyl-Sergeev duality. Finally, depict duality over $\mathbb{Z}$.

A combination of Bestvina–Brady Morse theory and an acyclic reflection group trick produces a torsion-free finitely presented Q-Poincaré duality group which is not the fundamental group of an aspherical closed ANR Q-homology manifold. The acyclic construction suggests asking which Q-Poincaré duality groups act freely on Q-acyclic spaces (i.e., which groups are FH(Q)). For example, the orbifold ...

In heterotic string theory compactified on T , the T-duality orbits of dyons of charge (Q,P ) are characterized by O(6, 22; R ) invariants Q, P 2 and Q · P together with a set of invariants of the discrete T-duality group O(6, 22; ZZ). We study the action of S-duality group on the discrete T-duality invariants and study its consequence for the dyon degeneracy formula. In particular we find that...

In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...

We give an argument showing that in N=4 supersymmetric gauge theories there exists at least one bound state saturating the Bogomol’nyi bound with electric charge p and magnetic charge q, for each p and q relatively prime, and we comment on the uniqueness of such state. This result is a necessary condition for the existence of an exact S-duality in N=4 supersymmetric theories. On leave of absenc...

The continuous extension of the discrete duality symmetry of the SchwarzSen model is studied. The corresponding infinitesimal generator Q turns out to be local, gauge invariant and metric independent. Furthermore, Q commutes with all the conformal group generators. We also show that Q is equivalent to the non—local duality transformation generator found in the Hamiltonian formulation of Maxwell...