Inverse scattering problems in several dimensions
Inverse scattering theory for Dirac operators
Invertible cohomological field theories and Weil-Petersson volumes
We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande....
Irreducible holonomy representations
Irreversibility in quantum mechanics.
Isometric immersions and induced geometric structures
In the paper under review, the author presents some results on the basis of the Nash-Gromov theory of isometric immersions and illustrates how the same results and ideas can be extended to other structures.
Isospectrality for quantum toric integrable systems
We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...
Isotropy representation of flag manifolds
A flag manifold of a compact semisimple Lie group is defined as a quotient where is the centralizer of a one-parameter subgroup of . Then can be identified with the adjoint orbit of in the Lie algebra of . Two flag manifolds and are equivalent if there exists an automorphism such that (equivalent manifolds need not be -diffeomorphic since is not assumed to be inner). In this article, explicit formulas for decompositions of the isotropy representation for all flag manifolds...
Itô calculus and quantisation of Lie bialgebras
Itô versus Woronowicz calculus in Itô Hopf algebras
Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator
Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional real Lie algebras. The Jacobi operators of these quantum algebras are explicitly calculated.
Jacobi vector fields and geodesic tubes in certain Kähler manifolds
Joint distributions and compatibility of observables in quantum logics
Jordan- and Lie geometries
In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic...
Jordan-Schwinger representations and factorised Yang-Baxter operators.
Jost solution and the spectrum of the discrete Dirac systems.
Jump processes and diffusions in relativistic stochastic mechanics
Junction type representations of the Temperley-Lieb algebra and associated symmetries.
-concircular vector fields and holomorphically projective mappings on Kählerian spaces
Kac-Moody algebras: An introduction for physicists