Characters of Reductive Groups over a Finite Field

This detailed work classifies complex irreducible representations of reductive groups over finite fields, utilizing advanced mathematical techniques.

In Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107, the author delves into the intricate world of representation theory, focusing on the classification of complex irreducible representations of reductive groups that possess a connected center over a finite field. This comprehensive study is significant for mathematicians and researchers interested in understanding the underlying structures of these groups and their representations.

The author employs etale intersection cohomology as a primary tool to systematically classify these representations. By integrating this advanced mathematical framework, the book provides a robust methodology for tackling the complexities involved in the classification process. Additionally, the text offers detailed insights into the representations of Weyl groups, which play a crucial role in understanding the broader context of reductive groups.

Overall, Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 serves as an essential resource for those engaged in the study of algebraic groups and representation theory. It not only presents a thorough classification but also enriches the reader's understanding of the relationships between various mathematical concepts, making it a valuable addition to the field.