相关论文: Mechanics on flag manifolds
We consider isotropic and Lagrangian embeddings of coadjoint orbits of compact Lie groups into products of coadjoint orbits. After reviewing the known facts in the case of $\mathrm{SU}(n)$ we initiate a similar study for $\mathrm{SO}$ and…
We perform further tests of the correspondence between spectral theory and topological strings, focusing on mirror curves of genus greater than one with nontrivial mass parameters. In particular, we analyze the geometry relevant to the…
In the present paper we study flag manifold sigma-models that admit a zero-curvature representation. It is shown that these models may be naturally considered as interacting (holomorphic and anti-holomorphic) $\beta\gamma$-systems. Besides,…
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of $\mathbb{Z}_2^k$-symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. We detail for…
We build on a characterization of inner functions $f$ due to Le, in terms of the spectral properties of the operator $V=M_f^*M_f$ and study to what extent the cyclicity on weighted Hardy spaces $H^2_\omega$ of the function $z \mapsto a-z$…
Motivated by the work of Abreu and Freitas, we study the invariant spectrum of the Laplace operator associated to hermitian line bundles endowed with invariant metrics over $\mathbb{p}^1$.
The Laplacian of a general trace polynomial function defined on the special orthogonal group $SO(N)$ is explicitly computed. An invariant flag of spaces generated by trace polynomials is constructed. The matrix of the Laplace-Beltrami…
We compute the spectral action of $SU(2)/\Gamma$ with the trivial spin structure and the round metric and find it in each case to be equal to $\frac{1}{|\Gamma|} (\Lambda^3 \hat{f}^{(2)}(0) - 1/4\Lambda \hat{f}(0))+ O(\Lambda^{-\infty})$.…
Let $(G_\epsilon)_{\epsilon>0}$ be a family of '$\epsilon$-thin' Riemannian manifolds modeled on a finite metric graph $G$, for example, the $\epsilon$-neighborhood of an embedding of $G$ in some Euclidean space with straight edges. We…
We study special Lagrangian fibrations of $\mathrm{SU}(3)$-manifolds, not necessarily torsion-free. In the case where the fiber is a unimodular Lie group $G$, we decompose such $\mathrm{SU}(3)$-structures into triples of solder 1-forms,…
It is known that the spin structure on a Riemannian manifold can be extended to noncommutative geometry using the notion of a spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in…
We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed as an operator-valued function of time…
We investigate the equivalence between spectral characteristics of the Laplace operator on a metric graph, and the associated unitary scattering operator. We prove that the statistics of level spacings, and moments of observations in the…
The action of the subgroup $\operatorname{G}_2$ of $\operatorname{SO}(7)$ (resp.\ $\operatorname{Spin}(7)$ of $\operatorname{SO}(8)$) on the Grassmannian space $M=\frac{\operatorname{SO}(7)}{\operatorname{SO}(5)\times\operatorname{SO}(2)}$…
The aim of this paper is to study a possible "boundary phenomenon" for Spinc Dirac operators in a special case. If you parametrise Spinc Dirac operators by a family of connections on a Spinc 4-manifold with boundary, this boundary inherits…
Hitchin shows that half-flat SU(3)-structures on a 6-dimensional manifold M can be lifted to parallel G_{2}-structure on the product $M\times\mathbb{R}$. We show that Hitchin's approach can also be used to construct nearly parallel…
Invariants for framed links in $S^3$ obtained from Chern-Simons gauge field theory based on an arbitrary gauge group (semi-simple) have been used to construct a three-manifold invariant. This is a generalization of a similar construction…
We compute three-point functions of general operators in the su(1|1) sector of planar N = 4 SYM in the weak coupling regime, both at tree-level and one-loop. Each operator is represented by a closed spin chain Bethe state characterized by a…
We investigate entanglement spectra of the SO(3) bilinear-biquadratic spin-1 chain, a model with phases exhibiting spontaneous symmetry breaking (both translation and spin rotation), points of enlarged symmetry, and a symmetry-protected…
We establish $L^q$ spectral cluster bounds for families of orthonormal functions associated to the Laplace-Beltrami operator on a compact Riemannian manifold. The metric is only assumed to be of class $C^s$, where $0\leq s\leq 2$.