Automorphic Forms and Applications: Denis Osipov (MIAN/NRU HSE)
The Seminar Automorphic Forms and Applications will take place on Dec 11 at 18:00 in the room 306
Denis Osipov (MIAN/NRU HSE) will give a talk «Discrete Heisenberg group and theta functions»
Abstract: The Heisenberg discrete group is a 3 by 3 group of upper triangular integer matrices with units on the diagonal. A.N. Parshin described the irreducible complex representations of the discrete Heisenberg group and calculated the traces of elements from the extended Heisenberg group, which is a semidirect product of the original Heisenberg group and the group of integers acting on these representations. The resulting traces are Jacobi theta functions. In the joint work of A.N. Parshin and the speakerthe discrete Heisenberg group was obtained from a two-dimensional local field associated with the flag of subvarieties on a two-dimensional arithmetic manifold, and the infinite-dimensional irreducible complex representation was naturally obtained from the space of distributions of the same two-dimensional local fields. In addition, the extended Heisenberg group acts on this representation in a natural way, the traces of the elements of which are Jacobi theta functions. I will tell about this circle of questions in my report.