Robinson-Schensted correspondence is one of the fundamental tools to understand the structure and representation theory of symmetric groups. In this talk, I will first briefly recall their construction and its relation to representation theory, focusing on the theory of Kazhdan-Lusztig and combinatorics of standard Young tableaux.
Meanwhile, there exists an affine analogue of this algorithm developed by Chmutov-Lewis-Pylyavskyy-Yudovina, based on the result of Shi, called the affine matrix-ball construction (abbreviated AMBC). I will discuss how this is related to the structure of (extended) affine symmetric groups. After this, if time permits, I will also discuss the Schutzenberger involution and its affine analogue.