LisMath Seminar 

20/05/2016, 16:00 — 17:00 — Room 6.2.33, Faculty of Sciences of the Universidade de Lisboa
Pedro Matos, Universidade de Lisboa

The Gelfand-Graev character of $\operatorname{GL}(n,q)$

In 1962, I.M. Gelfand and M.I. Graev constructed explicitly a character for $\operatorname{SL}(n,q$) and showed that it is multiplicity free [1]. In 1967, R. Steinberg generalised this construction for certain Chevalley-Dickson groups [2]. An even more general construction holds in the setting of finite groups of Lie type. In this talk, we define the Gelfand-Graev character for $\operatorname{GL}(n,q)$, and adapt the multiplicity free proof as given in [3]. For this, we make a quick introduction to some of the important tools needed from representation theory of associative algebras and finite groups. 

Bibliography

1. I. M. Gelfand, M. I. Graev, Construction of irreducible representations of simple algebraic groups over a finite field, Dokl. Akad. Nauk SSSR, 147 (1962).
2. R. Steinberg, Lectures on Chevalley Groups, Yale University, 1967.
3. R. W. Carter, Finite groups of Lie type: conjugacy classes and complex characters, Wiley Interscience, 1993. 

See also

Seminar.pdf