The local Langlands conjecture for \(p\)-adic \(\mathrm{GSpin}_{4}\), \(\mathrm{GSpin}_{6}\), and their inner forms. (English) Zbl 1384.22007
From the text: “In this article, we construct L-packets for the split general spin groups GSpin\({}_4\), GSpin\({}_6\) and their inner forms over a \(p\)-adic field \(F\) of characteristic 0, and more importantly, establish their internal structures in terms of characters of component groups, as predicted by the local Langlands conjecture (LLC). This establishes the LLC for the groups in question.”
”The construction of the L-packets is essentially an exercise in restriction of representations, thanks to the structure, as algebraic groups, of the groups we consider; however, proving the properties of the L-packets requires some deep results of Hiraga-Saito as well as Aubert-Baum-Plymen-Solleveld.”
The authors refer to the papers by K. Hiraga and H. Saito [Mem. Am. Math. Soc. 1013, iii-v, 97 p. (2012; Zbl 1242.22023)] and A.-M. Aubert et al. [Res. Math. Sci. 3, Paper No. 32, 34 p. (2016; Zbl 1394.22015)].
”The construction of the L-packets is essentially an exercise in restriction of representations, thanks to the structure, as algebraic groups, of the groups we consider; however, proving the properties of the L-packets requires some deep results of Hiraga-Saito as well as Aubert-Baum-Plymen-Solleveld.”
The authors refer to the papers by K. Hiraga and H. Saito [Mem. Am. Math. Soc. 1013, iii-v, 97 p. (2012; Zbl 1242.22023)] and A.-M. Aubert et al. [Res. Math. Sci. 3, Paper No. 32, 34 p. (2016; Zbl 1394.22015)].
Reviewer: Anatoly N. Kochubei (Kyïv)
MSC:
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
| 11S37 | Langlands-Weil conjectures, nonabelian class field theory |
| 20G25 | Linear algebraic groups over local fields and their integers |
| 22E35 | Analysis on \(p\)-adic Lie groups |
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