相关论文: Variational formulas on spaces of SL(2) Hitchin's …
Using the embedding of the moduli space of generalized GL(n) Hitchin's spectral covers to the moduli space of meromorphic abelian differentials we study the variational formulae of the period matrix, the canonical bidifferential, the prime…
We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…
We study the Hitchin morphism for higher dimensional varieties and show that, for a certain class of varieties which we call r-small, the set-theoretic image of the Hitchin morphism from the Dolbeault moduli space coincides with the…
It is shown that the map from the Jacobian of the spectral curve to the moduli of stable bundles of rank 2 is generically simply branched along an irreducible divisor. This observation falsifies the key step in the "abelianization of the…
Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times2$ matrix or second order scalar spectral problems. The theory…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
We describe certain Lagrangian fibrations by Prym varieties on holomorphic symplectic varieties that deform to compactifications of Sp-Hitchin systems.
The main result is an explicit expression for the Pressure Metric on the Hitchin component of surface group representations into PSL(n,R) along the Fuchsian locus. The expression is in terms of a parametrization of the tangent space by…
We study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then,…
In this paper after recalling some essential tools concerning the theory of differential forms in the Cartan, Hodge and Clifford bundles over a Riemannian or Riemann-Cartan space or a Lorentzian or Riemann-Cartan spacetime we solve with…
We present an alternative 2-parametric deformation $ GL(2)_{h,h'} $ , and construct the differential calculus on the quantum plane on which this quantum group acts. Also we give a new deformation of the two dimensional Heisenberg algebra
In this paper, we explore the structure of the Hitchin morphism for higher dimensional varieties. We show that the Hitchin morphism factors through a closed subscheme of the Hitchin base, which is in general a non-linear subspace of lower…
We define and parametrise so-called $\mathfrak{sl}(2)$-type fibres of the $\mathsf{Sp}(2n,\mathbb{C})$- and $\mathsf{SO}(2n+1,\mathbb{C})$-Hitchin system. These are (singular) Hitchin fibres, where the spectral curve induces a two-sheeted…
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed…
Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and…
We study two-parameter oscillator variations of the classical theorem on harmonic polynomials, associated with noncanonical oscillator representations of sl(n) and o(n). We find the condition when the homogeneous solution spaces of the…
An L2 theory of differential forms is proposed for the Banach manifold of continuous paths on Riemannian manifolds M furnished with its Brownian motion measure. Differentiation must be restricted to certain Hilbert space directions, the…
Using crystal basis, in the space of symmetric irreducible representations, we explicitly write invertible deforming functionals between the q-deformed universal enveloping algebra and the Lie algebras sl(n) and sp(2n).For sl(2) we obtain…
Two trace formulas for the spectra of arbitrary Hermitian matrices are derived by transforming the given Hermitian matrix $H$ to a unitary analogue. In the first type the unitary matrix is $e^{i(\lambda\II - H)}$ where $\lambda$ is the…
In this second part of our series of papers, we develop an abstract framework suitable for de Rham complexes that depend on a parameter belonging to an arbitrary Banach space. Our primary focus is on spectral perturbation problems and the…