相关论文: Traces of intertwiners for quantum groups and diff…

The main object considered in this paper is the trace function, defined as a suitably normalized trace of a product of intertwining operators for the Drinfeld-Jimbo quantum group, multiplied by the exponential of an element of the Cartan…

We modify and give complete proofs for the results of Etingof-Schiffmann-Varchenko on traces of intertwiners of untwisted quantum affine algebras in the opposite coproduct and the standard grading. More precisely, we show that certain…

This paper is a continuation of math.QA/9907181 and math.QA/9908115. We consider traces of intertwiners between certain representations of the quantized enveloping algebra associated to a semisimple complex Lie algebra g, which are twisted…

We show that the traces of $U_q(\widehat{\mathfrak{sl}}_2)$-intertwiners of Etingof-Schiffmann-Varchenko valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a…

The purpose of this paper is to introduce and study a q-analogue of the holonomic system of differential equations associated to the Belavin's classical r-matrix (elliptic r-matrix equations), or, equivalently, to define an elliptic…

Using {\it weighted traces} which are linear functionals of the type $$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$ defined on the whole algebra of (classical) pseudo-differential operators (P.D.O.s) and where $Q$ is some…

In our previous paper math.QA/9907181, to every finite dimensional representation V of the quantum group U_q(g), we attached the trace function F^V(\lambda,\mu), with values in End V[0], obtained by taking the (weighted) trace in a Verma…

Let $\Phi:V\to V\otimes U$ be an intertwining operator between representations of a simple Lie algebra (quantum group, affine Lie algebra). We define its generalized character to be the following function on the Cartan subalgebra with…

We use the $q$-characters to compute explicit expressions of the $R$-matrices for first fundamental representations of all types of twisted quantum affine algebras.

We initiate the study of a q-deformed geometry for quantum SU(2). In contrast with the usual properties of a spectral triple, we get that only twisted commutators between algebra elements and our Dirac operator are bounded. Furthermore, the…

The trace of intertwining operators over the level one irreducible highest weight modules of the quantum affine algebra of type A_{N-1} is studied. It is proved that the trace function gives a basis of the solution space of the qKZ equation…

This paper is to study what we call twisted regular representations for vertex operator algebras. Let $V$ be a vertex operator algebra, let $\sigma_1,\sigma_2$ be commuting finite-order automorphisms of $V$ and let…

We first construct an action of the extended double affine braid group $\mathcal{\ddot{B}}$ on the quantum toroidal algebra $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in untwisted and twisted types. As a crucial step in the proof, we obtain a…

Cherednik's quantum affine Knizhnik-Zamolodchikov equations associated to an affine Hecke algebra module M form a holonomic system of q-difference equations acting on M-valued functions on a complex torus T. In this paper the quantum affine…

We extend the graphical calculus developed in the first part of this paper to the parametrising spaces of quantum vertex operators. This involves a graphical implementation of the dynamical twist functor, which is a strict monoidal functor…

Positive twisted traces are mathematical objects that could be useful in computing certain parameters of superconformal field theories. The case when $\mathcal{A}$ is a $q$-Weyl algebra and $\rho$ is a certain antilinear automorphism of…

In this paper, we present an explicit construction of twisted traces for quantum Coulomb branches of conical theories. We develop an operator representation of the Coulomb branch algebra and use it to derive integral formulas for the…

The resonance relations are identities between coordinates of functions with values in tensor products of representations of the quantum group Uq(sl2). We show that the space of hypergeometric solutions of the associated qKZB equations is…

We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…

We construct explicitly the $q$-vertex operators (intertwining operators) for the level one modules $V(\Lambda_i)$ of the classical quantum affine algebras of twisted types using interacting bosons, where $i=0, 1$ for $A_{2n-1}^{(2)}$,…