nO and the inertial Langlands correspondence
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1152KbAbstractThis thesis is divided hermes kelly wallet replica
into two parts. The first one comes from the representation theory of reductive adic groups. The main motivation behind this part of the thesis is to find new explicit information and invariants of the types in general linear groups. Let be a non Archimedean local field and let be its ring of integers. We give an explicit description of cuspidal types on, with prime, in terms of orbits. We determine which of them are regular representations and we provide an example which shows that an orbit of a representation does not always determine whether it is a cuspidal type or not. At the same time we prove that a cuspidal type for a representation of is regular if and only if the normalised level of is equal to or for. The second part of the thesis comes from the theory of integer valued polynomials and simultaneous orderings. This is a joint work with Mikoaj Frczyk. The notion of simultaneous ordering was introduced by Bhargava in his early work on integer valued polynomials. Let be a number field and let be its ring of integers. Roughly speaking a simultaneous ordering is a sequence of elements from which is equidistributed modulo every power of every prime ideal in as well as possible. Bhargava asked which subsets of Dedekind domains admit simultaneous ordering. Together with Mikoaj Frczyk we proved that the only number field with admitting a simultaneous ordering is.