BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shraddha Srivastava (Uppsala University) DTSTART:20220505T060000Z DTEND:20220505T070000Z DTSTAMP:20260423T004729Z UID:ARCSIN/15 DESCRIPTION:Title: Diagram categories and reduced Kronecker coefficients\nby Shraddha Sri vastava (Uppsala University) as part of ARCSIN - Algebra\, Representations \, Combinatorics and Symmetric functions in INdia\n\n\nAbstract\nPartition algebras are a class of diagram algebras which naturally fit into a tower and the so called partition category provides a unified framework for the study of the algebras in the tower. The path algebra of the partition cat egory admits a triangular decomposition similar to a triangular decomposit ion of the universal enveloping algebra of a finite dimensional complex se misimple Lie algebra. In such a decomposition\, the direct sum of symmetri c group algebras plays a role analogous to Cartan subalgebra and this prov ides a natural approach to the representation theory of the partition cate gory. The tensor structure on the partition category induces a ring struct ure on the associated Grothendieck group. Reduced Kronecker coefficients f or symmetric groups appear as structure constants in the Grothendieck ring . \n\nIn this talk\, we discuss the partition category and its connection to reduced Kronecker coefficients (these are results of several authors). We introduce the multiparameter colored partition category where the Carta n subalgebra in the corresponding triangular decomposition is given by com plex reflection groups of type $G(r\,1\,n)$. The multiparameter colored pa rtition category also admits a tensor structure. If time permits\, we also relate the associated Grothendieck ring for this category with the ring o f symmetric functions. This talk is based on joint work with Volodymyr Maz orchuk.\n LOCATION:https://researchseminars.org/talk/ARCSIN/15/ END:VEVENT END:VCALENDAR