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 HPqn
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 Uq(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 AdG(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 AdG(t) is an orthogonal or symplectic Grassmannian. Then the stabilizer subgroup is not quantized as a quantum subgroup in Uq(𝔤). In our talk we consider quaternionic projective space HPn as a conjugacy class of the symplectic compact group G = Sp(n). We prove that 𝒪(t) is semi-simple and describe its simple objects, for one of two points t ∈ T ∩ HPn.