On the motive of \(G\) and the principal homomorphism \(\text{SL}_2\to\widehat G\)

DOI10.4310/AJM.1997.v1.n1.a8zbMath0942.20031MaRDI QIDQ1293776

Gross, Benedict H.

Publication date: 3 May 2000

Published in: The Asian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

\(L\)-functionsconnected reductive groupsadjoint representationsSteinberg representations\(L\)-groupslocal non-Archimedean fieldsdual motivesLanglands dual groupsprincipal homomorphisms

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Representations of Lie and linear algebraic groups over local fields (22E50) Langlands-Weil conjectures, nonabelian class field theory (11S37) Linear algebraic groups over local fields and their integers (20G25) Generalizations (algebraic spaces, stacks) (14A20)

Related Items

On Minuscule Representations and the Principal SL₂, Deformations of Galois representations and exceptional monodromy, Arithmetic invariants of discrete Langlands parameters, Algebraic modular forms, Formal degrees and adjoint 𝛾-factors, A rigid irregular connection on the projective line, Unnamed Item, Correction to “Formal degrees and adjoint 𝛾-factors”, Galois deformation spaces with a sparsity of automorphic points, Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations, Potential automorphy of \(\mathrm{GSpin}_{2n+1}\)-valued Galois representations