Duality and self-duality for dynamical quantum groups

Duality for Knizhnik-Zamolodchikov and Dynamical Operators

We consider the Knizhnik-Zamolodchikov and dynamical operators, both differential and difference, in the context of the $(\mathfrak{gl}_{k}, \mathfrak{gl}_{n})$-duality for the space of polynomials in $kn$ anticommuting variables. We show that the Knizhnik-Zamolodchikov and dynamical operators naturally exchange under the duality.

Duality for Knizhnik-Zamolodchikov and Dynamical Equations

We consider the Knizhnik-Zamolodchikov (KZ) and dynamical equations, both differential and difference, in the context of the (gl_k,gl_n) duality. We show that the KZ and dynamical equations naturally exchange under the duality.

Quasi-bialgebras and dynamical r-matrices

We study the relationship between general dynamical Poisson groupoids and Lie quasi-bialgebras. For a class of Lie quasi-bialgebras naturally compatible with a reductive decomposition, we extend the description of the moduli space of classical dynamical r-matrices of Etingof and Schiffmann. We construct, in each gauge orbit, an explicit analytic representative l. We translate the notion of duality for dynamical Poisson groupoids into a duality for Lie quasi-bialgebras. It is shown that duality maps the dynamical Poisson groupoid for l and a Lie quasi-bialgebra to the dynamical Poisson groupoid…

正交Howe对偶与动态（分裂）对称对

Orthogonal Howe duality and dynamical (split) symmetric pairs

受李代数相关动态结构启发，为分裂对称对引入动态融合、K-矩阵及Weyl群版本，研究(𝔰𝔬₂ₙ,Oₘ)-对偶性并证明𝔰𝔬₂ₙ侧标准算子与Oₘ侧对称对类似物可交换。

Quantum Deformations of the Self-Duality Equation and Conformal Twistors

A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group self-duality equation in the framework of the local gauge algebra of differential forms on $q$-twistor spaces. Quantum deformations of the general multi-instanton solutions are constructed. The corresponding noncommutative algebras of moduli are introduced. The general $q$-instanton connection is a function of the $q$-twistors and the $q$-moduli .

Differential Calculus on the Quantum Sphere and Deformed Self-Duality Equation

We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere $SU_q (2)/U(1) $. The $SU_q (2)$-spinor harmonics are treated as coordinates of the quantum sphere. We consider the gauge theory for the quantum group $SU_q (2)\times U(1) $ on the deformed Euclidean space $E_q (4)$. A $q$-generalization of the harmonic-gauge-field formalism is suggested . This formalism is applied for the harmonic (twistor) interpretation of the quantum-group self-duality equation (QGSDE). We consider the zero-curvature representation and the general construction of QGSDE-solutions in term…