Number Theory Seminar

To extend the Langlands program to covering groups, such as the metaplectic group, one needs to construct a dual group $G^\vee$ (a connected reductive group) and an L-group (an extension of the absolute Galois group, or Weil group, by $G^\vee$). In this talk I will introduce covering groups in a framework suggested by Brylinski and Deligne, and describe the construction of the dual group and L-group for such covering groups. To finish the talk, I will describe the current state of the art -- evidence that this L-group is the correct choice, and some open questions.