Speaker: Dr Kaustubh Mondal: IISER Pune

Title : A Finite Linear Dependence of Discrete Series Multiplicities

Abstract : Let $G$ be a non-compact connected semisimple Lie group with a compact Cartan subgroup and $\Gamma$ be a uniform lattice in $G$. In this talk, we will describe that an infinite set of discrete series multiplicities in $L^2(\Gamma \backslash G)$ can be determined from any finite subset satisfying a certain condition. This result leads to a refinement of the strong multiplicity one theorem for discrete series representations. We will conclude the talk by illustrating an application of this result in the context of spaces of holomorphic cusp forms. This is a joint work with Gunja Sachdeva.