Lifting automorphic representations on the double covers of orthogonal groups

Lifting Automorphic Representations on the Double Covers of Orthogonal Groups

Suppose that G and H are connected reductive groups over a number field F and that an L-homomorphism ρ : LG −→ LH is given. The Langlands functoriality conjecture predicts the existence of a map from the automorphic representations of G(A) to those of H(A). If the adelic points of the algebraic groups G, H are replaced by their metaplectic covers, one may hope to specify an analogue of the Lgro...

Automorphic Representations of Adele Groups

On Cartesian Products of Orthogonal Double Covers

Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex, where G is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of G and any two members share an edge whenever the corresponding vertices are adjacent in H and share no edges whenever the corresponding vertices are nonadjacent in H. In this paper, we are concerned with ...

Lifting Representations of Z - Groups

Let K be the kernel of an epimorphism G→ Z, where G is a finitely presented group. If K has infinitely many subgroups of index 2, 3 or 4, then it has uncountably many. Moreover, if K is the commutator subgroup of a classical knot group G, then any homomorphism from K onto the symmetric group S2 (resp. Z3) lifts to a homomorphism onto S3 (resp. alternating group A4).

Orthogonal double covers of complete bipartite graphs

Let H = {A1, . . . , An, B1, . . . , Bn} be a collection of 2n subgraphs of the complete bipartite graph Kn,n. The collection H is called an orthogonal double cover (ODC) of Kn,n if each edge of Kn,n occurs in exactly two of the graphs in H; E(Ai) ∩ E(Aj) = φ = E(Bi) ∩ E(Bj) for every i, j ∈ {1, . . . , n} with i = j, and for any i, j ∈ {1, . . . , n}, |E(Ai)∩E(Bj)| = 1. If Ai ∼= G ∼= Bi for al...