报告人：Jonas T. Hartwig（Iowa State University）
Reduction algebras are known by many names in the literature, including step algebras, Mickelsson algebras, Zhelobenko algebras, and transvector algebras, to name a few. In this talk we present some results about the diagonal reduction superalgebra A of the orthosymplectic Lie superalgebra osp(1|2). We prove that the ghost center (center plus anti-center) of A is generated by two central elements and one anti-central element (analogous to the Scasimir due to Lesniewski). We also classify all finite-dimensional irreducible representations of A. As an application we provide an explicit decomposition of an infinite-dimensional tensor product of osp(1|2)-representations.
This talk is based on joint work with Dwight Anderson Williams II.
Dr. Jonas T. Hartwig is currently Associate Professor of Mathematics at Iowa State University. He received his Ph.D. in 2008 from Chalmers University of Technology. He has held postdoctoral research positions at Korteweg-de Vries Institute for Mathematics at University of Amsterdam and Institute of Mathematics and Statistics at University of S?o Paulo, and was a Visiting Assisant Professor at University of California Riverside. Dr. Hartwig's research interests include representation theory for Lie algebras, quantum groups and related algebras, and connections to geometry and mathematical physics.