arXiv subjects

Vadim Ostapenko

Publications and source records attributed to Vadim Ostapenko.

3 recordsLinked to original sources

arXiv2016

Quantum exceptional group $G_2$ and its conjugacy classes

We construct quantization of semisimple conjugacy classes of the exceptional group $G=G_2$ along with and by means of their exact representations in highest weight modules of the quantum group $U_q(\mathfrak{g})$. With every point $t$ of a fixed maximal torus we associate a highest weight module $M_t$ over $U_q(\mathfrak{g})$ and realize the quantized polynomial algebra of the class of $t$ by linear operators on $M_t$. Quantizations corresponding to points of the same orbit of the Weyl group are isomorphic.

math.QA↗

arXiv2002

$\Ughr$ invariant quantization on some homogeneous manifolds

We consider a class of homogeneous manifolds over a simple Lie group which appears in the problem of classification of homogeneous manifolds with reductive subgroups of maximal rank as stabilizer of a point. We prove that any manifold of this class possesses a Poisson bracket admitting a quantization invariant (equivariant) with respect to the corresponding quantum group.

math.QA↗

arXiv2002

Equivariant quantization on quotients of simple Lie groups by reductive subgroups of maximal rank

We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation q uantizations equivariant under the action of $G$ and the corresponding quantum group. We also classify Poisson brackets relating to such quantizations.

math.QA↗