20 citations · 33 across the 6 of their papers we have counts for
5 papers · 2 filters
Quantum coadjoint orbits of GL(n) and generalized Verma modules
J. Donin, A. Mudrov
In our previous paper, we constructed an explicit GL(n)-equivariant quantization of the Kirillov--Kostant-Souriau bracket on a semisimple coadjoint orbit. In the present paper, we…
On universal solution to reflection equation
J. Donin, P. P. Kulish, A. I. Mudrov
For a given quasitriangular Hopf algebra $\Ha$ we study relations between the braided group $\tilde \Ha^*$ and Drinfeld's twist. We show that the braided bialgebra structure of $\t…
Equivariant quantization on quotients of simple Lie groups by reductive subgroups of maximal rank
Joseph Donin, Vadim Ostapenko
We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation q uantizations equivariant under t…
Explicit equivariant quantization on (co)adjoint orbits of $GL(n,\C)$
J. Donin, A. Mudrov
We present an explicit $\U_h\bigl(gl(n,\C)\bigr)$-equivariant quantization on coadjoint orbits of $GL(n,\C)$. It forms a two-parameter family quantizing the Poisson pair of the ref…
Reflection Equation, Twist, and Equivariant Quantization
J. Donin, A. Mudrov
We prove that the reflection equation (RE) algebra $\La_R$ associated with a finite dimensional representation of a quasitriangular Hopf algebra $\Ha$ is twist-equivalent to the co…