Let G be a reductive algebraic group of Q-rank one associated to a self-adjoint homogeneous cone defined over Q, and let Γ ⊂ G be a torsion-free arithmetic subgroup. Let d be the cohomological dimension of Γ. We present an algorithm to compute the action of the Hecke operators on H(Γ;Z). This generalizes the classical modular symbol algorithm, when Γ ⊂ SL2(Z), to a setting including Bianchi gro...

We define a notion of ghost centre of a Lie superalgebra g = g0 ⊕ g1 which is a sum of invariants with respect to the usual adjoint action (centre) and invariants with respect to a twisted adjoint action (“anticentre”). We calculate the anticentre in the case when the top external degree of g1 is a trivial g0-module. We describe the Harish-Chandra projection of the ghost centre for basic classi...

For a general self-adjoint Hamiltonian operator H0, defined on the Hilbert space L (IRn), we determine the set of all self-adjoint Hamiltonians H on L(IRn) that (dynamically) confine the system to an open set S ⊂ IRn while reproducing the action of H0 on an appropriate domain. We propose strategies for constructing these Hamiltonians explicitly and for n = 1 we prove that an important class amo...

In recent work ([KW1],[KW2]), Kostant and Wallach construct an action of a simply connected Lie group A ≃ C( n 2 ) on gl(n) using a completely integrable system derived from the Poisson analogue of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In [KW1], the authors show that A-orbits of dimension ( n 2 ) form Lagrangian submanifolds of regular adjoint orbits in gl(n). They describe ...

Certain properties of maximal abelian projection are derived which suggest that the fundamental and adjoint SU(2) string tensions are reproduced by singly and doubly charged abelian Wilson loops, respectively. Thus, abelian dominance, which has been observed for color sources (quarks) in the fundamental representation, can be extended to higher representations. Numerical evidence in support of ...

We study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in 2 and 4 dimensions, related to generalizations of the Bethe-Sommerfeld conjecture and the Ten Martini Problem, ...