The real-quaternionic indicator, also called the δ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely connected to the Frobenius-Schur indicator, which we call the ε indicator. It is interesting to compute the ε and δ indicators. The computation of the ε indicator is relatively straightforward. In fact, it has been proven in large generality t...

An example of a strong invariant of an admissible representation (by which I mean an invariant capable of splitting points in Ĝadm) is the distributional character of a representation. Let G be a reductive Lie group, (π,H) an irreducible admissible representation of G and HK is associated Harish-Chandra (g,K)-module, and let Θπ be its distributional character Θπ (f) ≡ TrH (∫ f (g)π (g) dg ) , ∀...

Let K be a totally real number field, π an irreducible cuspidal representation of GL2(K)\GL2(AK) with unitary central character, and χ a Hecke character of conductor q. Then L(1/2, π ⊗ χ) ≪ (Nq) 1 2 − 1 8 , where 0 6 θ 6 1/2 is any exponent towards the Ramanujan– Petersson conjecture (θ = 1/9 is admissible). The proof is based on a spectral decomposition of shifted convolution sums and a genera...

We consider sums of the form π∈Sn χ λ/µ (π) q inv(π) where χ λ/µ is a skew character of the symmetric group and inv(π) is the number of inversions of π. Our main result gives a lower bound on the number of factors of 1 + q and 1 − q which divide the above sum, and is shown to be sharp when λ/µ is a hook partition shape. Résumé Nous considérons des sommes de la forme

Rh(CO)2Cl(NHC) complexes of dipyrido-annelated N-heterocyclic carbenes were prepared. From the C-H coupling constant of the respective imidazolium salts and the N-C-N angle of the N-heterocyclic carbene (NHC), a weaker σ-donor character than that of typical unsaturated NHCs is expected. However, the IR stretching frequencies of their Rh(CO)2Cl complexes suggest an electron-donor character even ...

The Wall surgery obstruction groups have two interesting geometrically defined subgroups, consisting of the surgery obstructions between closed manifolds, and the inertial elements. We show that the inertia group In+1(π,w) and the closed manifold subgroup Cn+1(π,w) are equal in dimensions n+1 ≥ 6, for any finitely-presented group π and any orientation character w : π → Z/2. This answers a quest...

In this paper we present and state evidence for a conjecture on the existence and properties of new vectors for generic irreducible admissible representations of GSp(4, F ) with trivial central character for F a nonarchimedean field of characteristic zero. To summarize the conjecture, let O be the ring of integers of F and let P be the prime ideal of O. We define, by a simple formula, a sequenc...

Given a finite group G and its representation ρ, the corresponding McKay graph is Γ(G,ρ) whose vertices are irreducible representations of G; number edges between two π,τ dimHom (π⊗ρ,τ). The collection all graphs for given encodes, in sense, character table. Such were also used by to provide bijection subgroups SU(2) affine Dynkin diagrams types A,D,E, considering appropriate graphs.