Mathematical Sciences: Representations of Finite Reductive Groups: A Characteristic Free Approach Through q-Deformations

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This project is concerned with the representation theory of general linear groups and their quantizations. The principal investigator will investigate the Hecke algebras associated with Weyl groups in an effort to extend the work on q-Schur algebras and apply it to other groups of Lie type. This research is in the general area of the representation theory of finite classical groups. One of the main applications of group theory to other mathematical and scientific fields is in representation theory, and finite classical groups are a primary source of finite simple groups.