Related papers: On the universal R-matrix for the Izergin-Korepin …
We construct new $U_q(a^{(2)}_{2n-1})$ and $U_q(e^{(2)}_6)$ invariant $R$-matrices and comment on the general construction of $R$-matrices for twisted algebras. We use the former to construct $S$-matrices for $b^{(1)}_n$ affine Toda…
The affine Gaudin model, associated with an untwisted affine Kac-Moody algebra, is known to arise from a certain gauge fixing of 4-dimensional mixed topological-holomorphic Chern-Simons theory in the Hamiltonian framework. We show that the…
A new twisted deformation, U_z(so(4,2)), of the conformal algebra of the (3+1)-dimensional Minkowskian spacetime is presented. This construction is provided by a classical r-matrix spanned by ten Weyl-Poincare generators, which generalizes…
The classical Gindikin-Karpelevich formula appears in Langlands' calculation of the constant terms of Eisenstein series on reductive groups and in Macdonald's work on p-adic groups and affine Hecke algebras. The formula has been generalized…
We present generalizations of the spin Sutherland systems obtained earlier by Blom and Langmann and by Polychronakos in two different ways: from SU(n) Yang--Mills theory on the cylinder and by constraining geodesic motion on the N-fold…
We obtain the exact solutions for a family of spin-boson systems. This is achieved through application of the representation theory for polynomial deformations of the $su(2)$ Lie algebra. We demonstrate that the family of Hamiltonians…
Let G be a reductive algebraic group over a local field K or a global field F. It is well know that there exists a non-trivial and interesting representation theory of the group G(K) as well as the theory of automorphic forms on the…
We obtain integral representations for the wave functions of Calogero-type systems,corresponding to the finite-dimentional Lie algebras,using exact evaluation of path integral.We generalize these systems to the case of the Kac-Moody…
We name an indecomposable symmetrizable generalized Cartan matrix $A$ and the corresponding Kac--Moody Lie algebra ${\goth g} ^\prime (A)$ {\it of the arithmetic type} if for any $\beta \in Q$ with $(\beta | \beta)<0$ there exist $n(\beta…
We construct a relativistic scattering theory based on a q deformation and large string tension limit of the magnon S-matrix of the string world sheet theory in AdS_5 x S^5. The S-matrix falls naturally into a previously studied class…
We construct a generalised notion of Kac-Moody algebras using smooth maps from the non-compact manifolds ${\cal M}=$SL$(2,\mathbb R)$ and ${\cal M}=$ SL$(2,\mathbb R)/U(1)$ to a finite-dimensional simple Lie group $G$. This construction is…
In this paper, we define and study the classical $R$-matrix for vertex Lie algebra, based on which we propose to construct a new vertex Lie algebra. We give a systematic way to construct the $R$-matrix for affine Kac-Moody vertex Lie…
Ian Grojnowski has developed a purely algebraic way to connect the representation theory of affine Hecke algebras at an (l+1)-th root of unity to the highest weight theory of the affine Kac-Moody algebra of type A_l^(1). The present article…
We develop a general scheme to construct integrable systems starting from realizations in symmetric coboundary dynamical Lie algebroids and symmetric coboundary Poisson groupoids. The method is based on the successive use of Dirac reduction…
A description of the embedding of the universal Askey--Wilson algebra, AW(3), in $U_q(sl_2)^{\otimes 3}$ is given in terms of the universal R-matrix of $U_q(sl_2)$. The generators of the centralizer of $U_q(sl_2)$ in its three-fold product…
Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields…
We introduce a twisted version of $K$-theory with coefficients in a $C^*$-algebra $A$, where the twist is given by a new kind of gerbe, which we call Morita bundle gerbe. We use the description of twisted $K$-theory in the torsion case by…
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin$^c$-complex under consideration is allowed to be further twisted by certain natural exterior…
We study the A_k generalized model of the O(1) loop model on a cylinder. The affine Hecke algebra associated with the model is characterized by a vanishing condition, the cylindric relation. We present two representations of the algebra:…
We analyze the h-deformations of the Lorentz group and their associated spacetimes. We prove that they have a twisted character and give explicitly the twisting matrices. After studying the representations of one of the deformed spacetime…