On some supersingular representations of \(\mathrm{GL}_2 (\mathbb Q_{p^f})\)

DOI10.1016/j.jalgebra.2010.06.006zbMath1206.22010OpenAlexW2083839725MaRDI QIDQ615846

Yongquan Hu

Publication date: 7 January 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2010.06.006

zbMATH Keywords

Diagramssupersingular representationsLocal LanglandsSmooth admissible representation

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50)

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MULTIPLICITY ONE AT FULL CONGRUENCE LEVEL ⋮ Diagrams and Mod p Representations of p-adic Groups ⋮ The image of Colmez's Montreal functor ⋮ Gelfand-Kirillov dimension and mod \(p\) cohomology for \(\mathrm{GL}_2 \) ⋮ On some representations of the Iwahori subgroup ⋮ Representations of \(p\)-adic groups over commutative rings ⋮ The classification of irreducible admissible mod \(p\) representations of a \(p\)-adic \(\mathrm{GL}_n\) ⋮ Explicit description of irreducible \(\mathrm{GL}_2(\mathbb{Q}_p)\)-representations over \(\bar {\mathbf F}_{p}\) ⋮ ON THE EXISTENCE OF ADMISSIBLE SUPERSINGULAR REPRESENTATIONS OF -ADIC REDUCTIVE GROUPS ⋮ Valeurs spéciales de paramètres de diagrammes de Diamond ⋮ Diagrammes canoniques et représentations modulo p de GL₂(F) ⋮ Diagrams in the mod p cohomology of Shimura curves ⋮ Invariant elements for $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$ ⋮ Iwasawa modules and \(p\)-modular representations of GL2 ⋮ Towards a modulo 𝑝 Langlands correspondence for 𝐺𝐿₂

Cites Work

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• On the weights of mod \(p\) Hilbert modular forms
• On Serre's conjecture for mod \(\ell \) Galois representations over totally real fields
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Irreducible modular representations of GL\(_ 2\) of a local field
• Principal indecomposable representations for the group SL(2,q)
• Extensions for supersingular representations of $GL_2(Q_p)$

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