Jintai Ding

Degenerate Poisson Pencils on Curves: New Separability Theory

Abstract A review of a new separability theory based on degenerated Poisson pencils and the so-called separation curves is presented. This theory can be considered as an alternative to the Sklyanin theory based on Lax representations and the so-called spectral curves.In this paper, we establish the connection between the quantized W-algebra of

Integral Presentations for the Universal R-Matrix

{\frak sl}(2,1)

Factorization of the universalR-matrix for\(U_q \left( {\hat sl_2 } \right)^1 \)

and quantum parafermions of

On the FRTS Approach to Quantized Current Algebras

U_q(\hat {\frak sl}(2))

Commutative quantum current operators, semi-infinite construction and functional models

that a shifted product of the two quantum parafermions of

Drinfeld realization of quantum superalgebras and U q(̂(1,2))

U_q(\hat {\frak sl}(2))

Zeros and poles of quantum current operators and the condition of quantum integrability

generates the quantized W-algebra of

Quantum current operators-I: zeros and poles of quantum current operators and the condition of quantum integrability

{\frak sl}(2,1)

Quantum current operators-II: difference equations of quantum current operators and quantum parafermion construction

.

Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators

AbstractWe present an integral formula for the universal R-matrix of quantum affine algebra Uq