Recently, Kaletha introduced a class of supercuspidal representations, called regular supercuspidal representations, of a fairly general p-adic reductive group G, and studied their detailed properties. In particular, he constructed the local Langlands correspondence for regular supercuspidal representations.
In this talk, when G = GL(n), we shall show that the correspondence constructed by Kaletha coincides with Harris-Taylor’s one. A key part of the proof is the fact that regular supercuspidal representations of GL(n) are nothing but the representations previously studied in detail by Bushnell-Henniart and Tam (essentially tame representations). This is a joint work with Masao Oi (Kyoto University).

Note of the talk (PDF): https://www.dropbox.com/s/hnnnwr7mxfvc00r

The seminar was organized by Zoom.