Dmytro Matvieievskyi

Last Update 2022/11/21
My research lies in the area of geometric representation theory. Unipotent representations, quantizations of symplectic singularities and instances of symplectic duality are the topics especially interesting to me.
Currently I am working on studying the unipotent ideals and their properties. In a joint work with Ivan Losev and Lucas MasonBrown we propose a definition of a unipotent ideal using the canonical quantizations of some algebras associated with nilpotent orbits. An interesting question is be to analyze this definition and study the properties from the Langlands dual group side. For special unipotent representations we show that the question of special unipotent ideals can be considered as a specific case of symplectic duality. Studying the aforementioned duality, and extending this duality to all unipotent ideals are the questions I am trying to solve.
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