Hecke Algebras for Types of Quasisplit Unitary Groups over Local Fields in the Principal Series
[S.l. : s.n.]
Number of pages
Radboud University, 9 december 2020
Promotor : Heckman, G.J. Co-promotor : Solleveld, M.S.
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SubjectMathematical Physics; Mathematics
"An Explicit Local Langlands Conjecture for the Unitary Group The Langlands program has been around since it was originally proposed in the 1970’s, with far reaching goals of connecting the mathematical fields of number theory to geometry (representation theory). This thesis is focused on the local Langlands conjectures, which are a broad subset of this larger picture intending to look at this map in certain far-reaching but more specialized cases. The case being considered is that of the unitary group, a classical object in group theory and very common in physics and mathematics, and the specific tools used are those of Hecke algebras. Thus, as a main result, we have explicitly constructed certain Hecke algebras for the unitary groups, and shown them to be of a certain well-known type. We have then created analogous objects on the other side of the map, and successfully used this to show the local Langlands conjecture in this context."
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