Related papers: Two-point Functions in Affine SL(N) Current Algebr…
The strong dual space of linear continuous functionals on a weighted space G of infinitely differentiable functions defined on the real line is described in terms of their Fourier-Laplace transforms.
The space spanned by the characters of twisted affine Lie algebras admit the action of certain congruence subgroups of $SL(2,\mathbb{Z})$. By embedding the characters in the space spanned by theta functions, we study an…
In this paper we consider a strong-weak coupling duality of the N=2 super-Liouville field theory (SLFT). Without the self-duality found in other Liouville theories, the N=2 SLFT, we claim, is associated with a `dual' action by a…
We apply our previous work on Green's functions for the four-dimensional quaternionic Taub-NUT manifold to obtain a scalar two-point function on the homogeneously squashed three-sphere (otherwise known as the Berger sphere), which lies at…
The extended phase space method of Batalin, Fradkin and Vilkovisky is applied to formulate two dimensional gravity in a general class of gauges. A BRST formulation of the light-cone gauge is presented to reveal the relationship between the…
We study the structure of the category of integrable level zero representations with finite dimensional weight spaces of affine Lie algebras. We show that this category possesses a weaker version of the finite length property, namely that…
The general solution of the two-dimensional integrable generalization of the f-Toda chain with fixed ends is explicitly presented in terms of matrix elements of various fundamental representations of the SL(n|n-1) supergroup. The dominant…
This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor…
An action for two dimensional gravity conformally coupled to two dilaton-type fields is analysed. Classically, the theory has some exact solutions. These include configurations representing black holes. A semi-classical theory is obtained…
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…
We study a class of representations over the degenerate double affine Hecke algebra of gl_n by an algebraic method. As fundamental objects in this class, we introduce certain induced modules and study some of their properties. In…
This paper is devoted to study of integrable structures in superconformal field theory and more general coset CFT's related to the affine Yangian $\textrm{Y}\big(\widehat{\mathfrak{gl}}(2)\big)$. We derive the relation between the RLL and…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
Recently, exact agreement has been found between bulk and boundary three-point functions in AdS_3 x S^3 x T^4 with NSNS fluxes. This represents a non-trivial check of AdS/CFT correspondence beyond the supergravity approximation as it…
We continue the program initiated in hep-th/0411200 and calculate the algebra of the flat currents for the string on AdS_5 x S^5 background in the light-cone gauge with kappa-symmetry fixed. We find that the algebra has a closed form and…
Splint of root system of simple Lie algebra appears naturally in the study of (regular) embeddings of reductive subalgebras. It can be used to derive branching rules. Application of splint properties drastically simplifies calculations of…
We start by describing two of the main proposals for duality in Abelian gauge theories, namely $F$(ield strength)-duality approach and the $S$% -duality formalism. We then discuss how $F$-duality and $S$-duality can be applied to the case…
For any natural number $n$, the group $G_n$ of all invertible affine transformations of $n$-dimensional Euclidean space has, up to equivalence, just one square-integrable representation and the left regular representation of $G_n$ is a…
It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is…
In the paper, we introduce and calculate difference Fourier transforms on representations of the double affine Hecke algebras in polynomilas, polynomials multiplied by the Gaussian, and various spaces of delta-functions including…