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Abstract

During the 2010's, Elias and Williamson constructed the diagrammatic Hecke category. This categorifies the Hecke algebra, and allows one to study certain polynomials showing up in the Hecke algebra, called Kazhdan-Lusztig polynomials, which are crucial to representation theory. In my thesis I construct an analogous category, called the diagrammatic spherical category. This categorifies a certain module over the Hecke algebra, called the spherical module, and allows us to study spherical Kazhdan-Lusztig polynomials. In this talk, I will motivate the study of Kazhdan-Lusztig polynomials, and describe the construction of the diagrammatic spherical category.