Let π be a cusp form on GL(2) over a number field F and let E be a quadratic extension of F . Denote by πE the base change of π to E and by Ω a unitary character of AE/E ×. We use the relative trace formula to give an explicit formula for L(1/2, πE ⊗ Ω) in terms of period integrals of GrossPrasad test vectors. We give an application of this formula to equidistribution of geodesics on a hyperbol...

The reaction of MesP=CPh2 with the least sterically demanding N-heterocyclic carbene (NHC = IMe) results in formation of the 'abnormal' (C(4)-substituted) 4-phosphino-NHC (1). In contrast, reaction with Me2IMe gives the unprecedented 'normal' C(2) adduct, Me2IMe → P(Mes)=CPh2 (2). Particularly striking is the asymmetric and weak bonding of the NHC to the P=C moiety in 2. DFT calculations indica...

In the title compound, C(9)H(12)Cl(2)N(4), the piperidine ring adopts a chair conformation. The electron delocalization of the molecule is indicated by the similar C⋯N distances within the triazine ring and by the double-bond character of the C=N triazine-piperidine connectivity. Weak intra-molecular C-H⋯N hydrogen bonds link the two rings within the mol-ecule, which exhibits a pseudo-mirror pl...

Last time we defined the maximal torus T and Weyl group W (G,T ) for a compact, connected Lie group G and explained that our goal is to relate the representation theory of T to that of G. One aspect of the representation theory of T and of G for which there is a simple relation is that of their representation rings. Consider representations π of a compact Lie group G on complex vector spaces an...

We report on results of recent studies of collisions of low-energy electrons with nucleobases and other DNA constituents. A particular focus of these studies has been the identification and characterization of resonances that play a role in electron attachment leading to strand breaks in DNA. Comparison of the calculated resonance positions with results of electron transmission measurements is ...

We study asymptotics of an irreducible representation of the symmetric group Sn corresponding to a balanced Young diagram λ (a Young diagram with at most O( √ n) rows and columns) in the limit as n tends to infinity. We find an optimal asymptotic bound for characters χ(π). Our main achievement is that—contrary to previous results in this direction—we do not assume that the length |π| of the per...

In the title compound, C35H32N4, the C-N bond lengths in the guanidine part are 1.286 (3), 1.387 (2) and 1.414 (2) Å, indicating double- and single-bond character. The N-C-N angles are 114.48 (17), 118.78 (17) and 126.72 (17)°, showing a deviation of the CN3 plane from an ideal trigonal-planar geometry. The carbazole ring system is almost planar (r.m.s. deviation = 0.002 Å). In the crystal, mol...

Let be a compact orientable surface with genus g and n boundary components ∂1, . . . , ∂n. Let b = (b1, . . . , bn) ∈ [−2, 2]n. Then the mapping class group Mod( ) acts on the relative SU(2)-character varietyXb := Homb(π , SU(2))/SU, comprising conjugacy classes of representations ρ with tr(ρ(∂i)) = bi. This action preserves a symplectic structure on the open dense smooth submanifold of Homb(π ...

Let Σ be a compact orientable surface with genus g and n boundary components ∂1, . . . , ∂n. Let b = (b1, . . . , bn) ∈ [−2, 2]. Then the mapping class groupMod(Σ) acts on the relative SU(2)-character variety Xb := Homb(π, SU(2))/SU(2), comprising conjugacy classes of representations ρ with tr(ρ(∂i)) = bi. This action preserves a symplectic structure on the open dense smooth submanifold of Homb...

Certain “index shifting operators” for local and global representations of the Jacobi group are introduced. They turn out to be the representation theoretic analogues of the Hecke operators Ud and Vd on classical Jacobi forms, which underlie the theory of Jacobi oldand new-forms. Further analogues of these operators on spaces of classical elliptic cusp forms are also investigated. In view of th...