Chennai Mathematical Institute


Seminar on Algebraic Geometry: Steinberg tensor product theorem and Steinberg representation
Dr. S. Senthamarai Kannan
Chennai Mathematical Institute.


The $G$ module of Global sections of a line bundle on $G/B$ is not necessarily irreducible in positive characteristic . But for a given prime $p$ and for any positive integer $n$ sections given by the character $p^{n}-1(\rho)$ is irreducible. These modules are called Steinberg modules. Any irreducible module in positive characteristic is a tensor product of finitely many restricted irreducible $G$- modules. The seminar is on describing these two theorems of Steinberg.