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Math & Stats Algebra & Geometry Seminar
Monday, March 3, 2025

Time: 4:30 p.m.  Place: Jeffery Hall, Room 116

Speaker: Yaolong Shen (University of Ottawa)

Title: Quantum supersymmetric pairs and ıSchur duality

Abstract: Let g be a semisimple Lie algebra and θ be an involution of g. The quantization (U_q(g),U^ı) of the symmetric pair (g,g^θ) was systematically developed by Letzter, where U_q(g) is the Drinfeld-Jimbo quantum group, and U^ı is a coideal subalgebra of it. We usually refer U^ı as the ıquantum group. Over the last decade, many fundamental constructions in quantum groups have been generalized to ıquantum groups by Wang and his collaborators. In this talk, we will discuss the super analog of U^ı and introduce one specific family which unites ıquantum groups (non-super) of type AI and AII. We will also demonstrate an ıSchur duality between this specific family and the q Brauer algebra. This duality can be viewed as a quantization of the classical duality between the orthosymplectic Lie superalgebra and the Brauer algebra. This is joint work with Weiqiang Wang