A connected reductive algebraic group G is said to be an l-adic algebraic monodromy group for ΓQ if there is a continuous homomorphism Gal(Q/Q)→ G(Ql) with Zariski-dense image. In this paper, we give a classification of connected l-adic algebraic monodromy groups for Gal(Q/Q), in particular producing the first such examples for SLn,Sp2n,Spinn and E sc 6 . To do this, we start with a mod-l repre...

Euler-Poincaré functions and pseudo-coefficients are important tools in harmonic analysis since they help to single out a given representation in direct integrals or sums. Given a real reductive groupG that admits a compact Cartan subgroup, these functions can be attached to a given finite dimensional representation τ of a maximal compact subgroup K. In [10] a construction was given in the case...

We prove an explicit formula for the invariant μ(g) for finite-dimensional semisimple, and reductive Lie algebras g over C. Here μ(g) is the minimal dimension of a faithful linear representation of g. The result can be used to study Dynkin’s classification of maximal reductive subalgebras of semisimple Lie algebras.

Let G be a split reductive group with dim⁡Z(G)≤1. We show that for any prime p is large enough relative to G, there finitely ramified Galois representation ρ:ΓQ→G(Zp) open image. also given integer e, if the index of irregularity at most e and then only image, generalizing theorem Ray [8]. The first type constructed by lifting suitable into G(Fp) using Fakhruddin–Khare–Patrikis [4], second vari...

For an essentially tame supercuspidal representation $\pi$ of a connected reductive $p$-adic group $G$, we establish two distinct and complementary sufficient conditions for the irreducible components its restriction to maximal compact subgroup occur in $G$ which is not inertially equivalent $\pi$. These results are further formulated terms geometry Bruhat-Tits building fixed points under actio...

In this paper, we study left-invariant Einstein-like metrics on the compact Lie group G. Assume that there exist two subgroups, H⊂K⊂G, such G/K is a compact, connected, irreducible, symmetric space, and isotropy representation of G/H has exactly inequivalent, irreducible summands. We prove left metric ⟨·,·⟩t1,t2 G defined by first equation, must be an A-metric. Moreover, groups do not admit non...

The Selberg-Arthur trace formula is one of the tools available for approaching the conjecture of global functoriality in the Langlands program. Global functoriality is described within this volume in [Kn2]. We start with reductive groups G and H, say over the rationals Q for simplicity. We assume that G is quasisplit, and we suppose that we are given an L homomorphism ψ : H → G. From an automor...