# Andrey Mudrov: Pseudo-parabolic categories over HP_q^n

Andrey Mudrov (University of Leicester, United Kingdom) will give a talk titled: Pseudo-parabolic categories over **H***P _{q}^{n}*

Abstract: With every point in a maximal torus *T* of a simple algebraic group *G* one can associate a full subcategory 𝒪(*t*) in the category 𝒪 of modules over the corresponding quantum group *U _{q}*(𝔤). It is closed under tensoring with finite-dimensional modules. If this category is semisimple, then it is equivalent to the category of equivariant quantum vector bundles over the conjugacy class Ad

_{G}(

*t*) passing through

*t*. Then the modules from 𝒪(

*t*) play a role of their “representations”. A case of special interest is when the centralizer subgroup of

*t*is not Levi, e.g. when Ad

_{G}(

*t*) is an orthogonal or symplectic Grassmannian. Then the stabilizer subgroup is not quantized as a quantum subgroup in

*U*(𝔤). In our talk we consider quaternionic projective space

_{q}**H**

*P*as a conjugacy class of the symplectic compact group

^{n}*G*=

*Sp*(

*n*). We prove that 𝒪(

*t*) is semi-simple and describe its simple objects, for one of two points

*t*∈

*T*∩

**H**

*P*.

^{n}