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Abstract
Let F be a finite extension of Q_p. A mod p local Langlands correspondence is known for GL_2(Q_p) and believed to exist between mod p
representations of the absolute Galois group of F and certain mod p
representations of GL_n(F) for arbitrary F and n. A major obstacle to the study of the correspondence is that the supersingular mod p representations of GL_n(F), which by recent work of Herzig are known to be the building blocks of the mod p representation theory of this group, are very poorly understood. After an introduction to the mod p representation theory of GL_n(F), we will discuss recently discovered obstacles to understanding the supersingular representations, as well as what is known.
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