Résume | In the representation theory of reductive groups in positive characteristic, there is a very special class of objects called tilting modules. Two important theorems state that the class of tilting modules is closed under tensor product and restriction to Levi subgroups.
Similarly, on (generalized) flag varieties, there is a special class of geometric objects called parity sheaves. I will explain two newer theorems that are analogues of the tensor product and restriction theorems mentioned above.
The main goal of the talk will be to explain how these two pictures fit together.
This is based on joint work with Daniel Juteau and Geordie Williamson. |