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Quantum Groups

- N. Reshetikhin, T. Johnson-Freyd
- Mathematics
- 1993

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions… Expand

Quantization of Lie Groups and Lie Algebras

- L. Faddeev, N. Reshetikhin, L. Takhtajan
- Mathematics
- 24 September 1987

Invariants of 3-manifolds via link polynomials and quantum groups

- N. Reshetikhin, V. Turaev
- Mathematics
- 1 December 1991

The aim of this paper is to construct new topological invariants of compact oriented 3-manifolds and of framed links in such manifolds. Our invariant of (a link in) a closed oriented 3-manifold is a… Expand

Ribbon graphs and their invaraints derived from quantum groups

- N. Reshetikhin, V. Turaev
- Mathematics
- 1990

The generalization of Jones polynomial of links to the case of graphs inR3 is presented. It is constructed as the functor from the category of graphs to the category of representations of the quantum… Expand

The q-characters of representations of quantum affine algebras and deformations of W-algebras

- E. Frenkel, N. Reshetikhin
- Mathematics
- 8 October 1998

We propose the notion of q-characters for finite-dimensional representations of quantum affine algebras. It is motivated by our theory of deformed W-algebras. We show that the q-characters give rise… Expand

Quantum affine algebras and holonomic difference equations

- I. Frenkel, N. Reshetikhin
- Mathematics
- 1 May 1992

AbstractWe derive new holonomicq-difference equations for the matrix coefficients of the products of intertwining operators for quantum affine algebra representations of levelk. We study the… Expand

Multiparameter quantum groups and twisted quasitriangular Hopf algebras

- N. Reshetikhin
- Mathematics
- 1 November 1990

It is shown how multiparameter quantum groups can be obtained from twisted Hopf algebras.

Deformations of W-algebras associated to simple Lie algebras

- E. Frenkel, N. Reshetikhin
- Mathematics
- 4 August 1997

Deformed W-algebra Wq,t(g) associated to an arbitrary simple Lie alge- bra g is defined together with its free field realizations and the screening operators. Explicit formulas are given for… Expand

Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras

- A. Kirillov, N. Reshetikhin
- Mathematics
- 1 November 1990

New combinatorial formulas are obtained for the multiplicities in the decomposition of the tensor product of the representations of simple Lie algebras into irreducible components.

q-Weyl group and a multiplicative formula for universalR-matrices

- A. Kirillov, N. Reshetikhin
- Mathematics
- 1 November 1990

We define theq-version of the Weyl group for quantized universal enveloping algebras of simple Lie group and we find explicit multiplicative formulas for the universalR-matrix.

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