[PDF] On certain supercuspidal representations of $SL_n(F)$ associated with tamely ramified extensions: the formal degree conjecture and the root number conjecture | Semantic Scholar

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Corpus ID: 237485495

On certain supercuspidal representations of $SL_n(F)$ associated with tamely ramified extensions: the formal degree conjecture and the root number conjecture

@inproceedings{Takase2021OnCS,
title={On certain supercuspidal representations of \$SL\_n(F)\$ associated with tamely ramified extensions: the formal degree conjecture and the root number conjecture},
author={Koichi Y. Takase},
year={2021}
}

1.1 Let F/Qp be a finite extension with p 6= 2 whose integer ring OF has unique maximal ideal pF wich is generated by ̟F . The residue class field F = OF /pF is a finite field of q-elements. The Weil group of F is denoted by WF which is a subgroup of the absolute Galois group Gal(F/F ) where F is a fixed algebraic closure of F in which we will take the algebraic extensions of F . Let G be a connected semi-simple linear algebraic group defined over F . For the sake of simplicity, we will assume… Expand

Let G be a reductive algebraic group over the local field k. The local Langlands conjecture predicts that the irreducible complex representations π of the locally compact group G(k) can be… Expand

The notion of depth is defined by Moy-Prasad [MP2]. The notion of a generic character will be defined in §9. When G = GLn or G is the multiplicative group of a central division algebra of dimension n… Expand