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