Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/214513
Title: AFFINE CELLULARITY OF THE ASYMPTOTIC J-RING OF CERTAIN TWO-SIDED CELLS IN TYPE A
Authors: KOH SHIWEI ISAAC
Keywords: Representation, theory, algebra, Hecke, algebra
Issue Date: 20-Oct-2021
Citation: KOH SHIWEI ISAAC (2021-10-20). AFFINE CELLULARITY OF THE ASYMPTOTIC J-RING OF CERTAIN TWO-SIDED CELLS IN TYPE A. ScholarBank@NUS Repository.
Abstract: Graham and Lehrer have defined cellular algebras and developed a theory that allows in particular classification of simple representations of finite dimensional cellular algebras. In the original paper, many classes of finite dimensional algebra, including Hecke algebra of type A, were proven to be cellular. Geck have proven that all Hecke algebras of finite type are cellular. Xi and Koenig has extended the framework of cellular algebras to algebras that need not be finite dimensional over a field. They introduced a generalisation of cellular algebra, affine cellular algebras, and they shown that extended affine Hecke algebra of type A are affine cellular. In this report, we will show that the asymptotic J-ring of type A , has certain subalgebras, corresponding to certain two-sided cells, that are affine cellular. In our second chapter, we will set up the necessary preliminaries needed. In the third chapter, we will talk about the asymptotic $J$-ring of the lowest two-sided cell of type $A$, before proving our main result. We will compute some example, and end our report with a conjecture for future work.
URI: https://scholarbank.nus.edu.sg/handle/10635/214513
Appears in Collections:Master's Theses (Open)

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