Time: 11:00--12:00 Wed. (Melbourne local time) for 2026S1.
Venue: Peter Hall 107
Main organisers: Alex Ghitza, Simon Marshall, Chenyan Wu
We have a more relaxed seminar schedule for 2026S1 due to teaching commitments.
Please go to the Number Theory Research Group website where you can find a link to join our mailing list.
The theory of automorphic forms sometimes requires working with covers of reductive groups, rather than with linear algebraic groups. For example, the Jacobi theta function naturally lives on the metaplectic group, a double cover of SL2, which is not linear. This motivates the study of representations of covers of p-adic reductive groups.
For such covering groups one would like to prove a local Langlands correspondence (LLC). In the case of linear groups, the LLC was established for the principal Bernstein block by combining the Borel-Casselman Theorem, which reduces the problem to the representation theory of affine Hecke algebras, with the work of Kazhdan-Lusztig on the representation theory of these algebras.
To extend this result to covering groups one must prove an analog of the Borel-Casselman Theorem. For tame covers this was accomplished by Savin, but the non-tame case has remained open. In this talk, I will describe recent joint work with Shuichiro Takeda in which we prove an analog of the Borel-Casselman Theorem for non-tame double covers.