30 citations · 94 across the 17 of their papers we have counts for
17 papers
An approach to annihilators in the context of vector field Lie algebras
Charles H. Conley, William Goode
We present a general method for describing the annihilators of modules of Lie algebras under certain conditions, which hold for some tensor modules of vector field Lie algebras. As…
Shadows of rationals and irrationals: supersymmetric continued fractions and the super modular group
Charles H. Conley, Valentin Ovsienko
This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric objects are defined over supercommutative rings of coefficients, and we consider an integ…
The vibrational modes of simplicial molecules
Charles H. Conley, Jon Erickson
Consider a "simplicial molecule": equal point masses placed at the vertices of a regular -simplex, connected by identical springs. We apply the represent…
Counting quiddities of polygon dissections
Charles H Conley, Valentin Ovsienko
We formulate the following general problem. To the best of our knowledge, it is open and has not previously been considered. It seems (at least to us!) to be difficult; at any rate…
Quiddities of polygon dissections and the Conway-Coxeter frieze equation
Charles H. Conley, Valentin Ovsienko
We study a matrix equation arising naturally in the theory of Coxeter frieze patterns. It is formulated in terms of the generators of the group $\mathrm{PSL}(2,\mathbb…
Lagrangian configurations and symplectic cross-ratios
Charles Conley, Valentin Ovsienko
We consider moduli spaces of cyclic configurations of lines in a -dimensional symplectic vector space, such that every set of consecutive lines generates a Lagrangian s…
Rotundus: triangulations, Chebyshev polynomials, and Pfaffians
Charles Conley, Valentin Ovsienko
We introduce and study a cyclically invariant polynomial which is an analog of the classical tridiagonal determinant usually called the continuant. We prove that this polynomial ca…
Factorizations of relative extremal projectors
Charles H. Conley, Mark R. Sepanski
We survey earlier results on factorizations of extremal projectors and relative extremal projectors and present preliminary results on non-commutative factorizations of relative ex…
Quantization and injective submodules of differential operator modules
Charles H. Conley, Dimitar Grantcharov
The Lie algebra of vector fields on acts naturally on the spaces of differential operators between tensor field modules. Its projective subalgebra is isomorphic to …
Centers and characters of Jacobi group-invariant differential operator algebras
Charles H. Conley, Rabin Dahal
We study the algebras of differential operators invariant with respect to the scalar slash actions of real Jacobi groups of arbitrary rank. These algebras are non-commutative and a…
Equivalence classes of subquotients of supersymmetric pseudodifferential operator modules
Charles H. Conley
We study the equivalence classes of the non-resonant subquotients of spaces of pseudodifferential operators between tensor density modules over the 1|1 superline, as modules of the…
Equivalence classes of subquotients of pseudodifferential operator modules
Charles H. Conley, Jeannette M. Larsen
Consider the spaces of pseudodifferential operators between tensor density modules over the line as modules of the Lie algebra of vector fields on the line. We compute the equivale…
Linear differential operators on contact manifolds
Charles H. Conley, Valentin Ovsienko
We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg cal…
Harmonic Maaß-Jacobi forms of degree 1 with higher rank indices
Charles H. Conley, Martin Raum
We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of…
Quantizations of modules of differential operators
Charles H. Conley
Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projectiv…
Symmetric Spaces in Supergravity
S. Ferrara, A. Marrani
We exploit the relation among irreducible Riemannian globally symmetric spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions. IRGS appear as scalar manifolds…
Conformal symbols and the action of contact vector fields over the superline
Charles H. Conley
Let K be the Lie superalgebra of contact vector fields on the supersymmetric line. We compute the action of K on the modules of differential and pseudodifferential operators betwee…