欧几里得空间中Hodge-de Rham系统的正交Appell基

欧几里得空间中Hodge-de Rham系统的Gelfand-Tsetlin基

The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces

本文的主要目的是为欧几里得空间R^m中Hodge-de Rham系统的k-齐次多项式解空间构造取s-向量空间值的显式正交基。实际上，我们甚至用盖根堡多项式来描述这种空间的所谓的Gelfand-Tsetlin基。作为应用，我们得到了R^m中广义Moisil-Theodoresco方程组齐次解空间的正交基的计算方法.

广义Moisil-Theodoresco系统和Hodge-de Rham系统的多项式解

On polynomial solutions of generalized Moisil-Theodoresco systems and Hodge-de Rham systems

研究广义Moisil-Theodoresco（GMT）系统的多项式解与Hodge-de Rham系统的多项式解之间的关系，并利用这些关系描述GMT系统的多项式解.我们将GMT系统的齐次解空间在群O（m）的作用下分解成不可约的块，并用它们的最高权来刻画各个块，计算它们的维数.

欧几里得空间中Hodge-de Rham系统的Fischer分解

The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces

旋量多项式的经典Fischer分解是欧几里得空间R^m中Dirac方程解的一个关键结果。众所周知，它可以被理解为关于Pin群Pin（m）的所谓L作用的不可约分解。但是，在Clifford代数值多项式上，我们也可以考虑Pin（m）的H作用。本文给出了H-作用的Fischer分解。事实证明，在这种情况下，基本构建块是Hodge-de Rham系统的齐次解空间。此外，它表明，Fischer分解的H-作用，甚至可以被视为一个经典的细化。

Towards a L 2 cohomology theory for Hodge modules on infinite covering spaces: L 2 constructible cohomology and L 2 de Rham cohomology for coherent D-modules

This article constructs Von Neumann invariants for constructible complexes and coherent D-modules on compact complex manifolds, generalizing the work of the author on coherent L 2-cohomology. We formulate a conjectural generalization of Dingoyan's L 2-Mixed Hodge structures in terms of Saito's Mixed Hodge Modules and give partial results in this direction. 2020 AMS Classification: 32J27.

Frölicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds

For complex parallelisable manifolds $Γ\backslash G$, with $G$ a solvable or semisimple complex Lie group, the Frölicher spectral sequence degenerates at the second page. In the solvable case, the de-Rham cohomology carries a pure Hodge structure. In contrast, in the semisimple case, purity depends on the lattice, but there is always a direct summand of the de Rham cohomology which does carry a pure Hodge structure and is independent of the lattice.

Harmonic forms and the Rumin complex on Sasakian manifolds

We show that the kernel of the Rumin Laplacian agrees with that of the Hodge-de Rham Laplacian on compact Sasakian manifolds. As a corollary, we obtain another proof of primitiveness of harmonic forms. Moreover, the space of harmonic forms coincides with the sub-Riemann limit of Hodge-de Rham Laplacian when its limit converges. Finally, we express the analytic torsion function associated with the Rumin complex in terms of the Reeb vector field.