We consider restrictions along closed geodesics and geodesic circles for eigenfunctions of the Laplace-Beltrami operator on a compact hyperbolic Riemann surface. We obtain a non-trivial bound on the L-norm of such restrictions as the eigenvalue tends to infinity. We use methods from the theory of automorphic functions and in particular the uniqueness of invariant functionals on irreducible unit...

We construct star-products on the co-adjoint orbit of the Lie group Aff(C) of affine transformations of the complex line and apply them to obtain the irreducible unitary representations of this group. These results show the effectiveness of the Fedosov quantization even for groups which are neither nilpotent nor exponential. Together with the result for the group Aff(R) (see [5]), we thus have ...

We give a constructive classification of the positive energy (lowest weight) unitary irreducible representations of the D = 6 superconformal algebras osp(8 * /2N). Our results confirm all but one of the conjectures of Minwalla on this classification. Our main tool is the explicit construction of the norms of the states that has to be checked for positivity. We give also the reduction of the fou...

Let G = Aut(T ) be the group of automorphisms of a homogeneous tree T , and let Γ be a lattice subgroup of G. Let π be the tensor product of two spherical irreducible unitary representations of G. We give an explicit decomposition of the restriction of π to Γ. We also describe the spherical component of π explicitly, and this decomposition is interpreted as a multiplication formula for associat...

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of...

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of...

It is known that the defining relations of the orthosymplectic Lie superalgebra osp(1|2n) are equivalent to the defining (triple) relations of n pairs of paraboson operators bi . In particular, the “parabosons of order p” correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V (p) of osp(1|2n). Recently we constructed these representations V (p) giving the expl...

A near-representation of a group G is a map M : G → GL(V ), where V is a complex linear space and Mgh ≈MgMh for all g, h ∈ G, i.e. M is approximately a homomorphism. Analogously to the representation theory of finite groups, we investigate the properties of nearrepresentations and show that they are equivalent to unitary nearrepresentations, and can be split to stably irreducible constituents. ...

I present several applications of the Dirac inequality to determination isolated unitary representations and associated “spectral gaps” in case unramified principal series. The method works particularly well order attach irreducible large nilpotent orbits (e.g., regular, subregular) Langlands dual complex Lie algebra. results could be viewed as a p-adic analogue Salamanca-Riba’s classification ...

Let F be a nonarchimedean local field of odd residual characteristic p. We classify finite-dimensional simple right modules for the pro-pIwahori-Hecke algebra HC(G, I(1)), where G is the unramified unitary group U(2, 1)(E/F ) in three variables. Using this description when C = Fp, we define supersingular Hecke modules and show that the functor of I(1)-invariants induces a bijection between irre...