Related papers: Dirac Cohomology for the Cubic Dirac Operator

We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…

We introduce algebraic families of Dirac operators for the deformation family (and other related families) associated with a real reductive Lie group that interpolates the reductive group and the corresponding Cartan motion group. We prove…

In this paper, we define and develop a cohomology and deformation theories of Jacobi-Jordan algebras. We construct a cohomology based on two operators, called zigzag cohomology, and detail the low degree cohomology spaces. We describe the…

We define a family of Dirac operators for the Dunkl angular momentum algebra depending on certain central elements of the group algebra of the Pin cover of the Weyl group inherent to the rational Cherednik algebra. We prove an analogue of…

In the 1960s, Dwork developed a p-adic cohomology theory of de Rham type for varieties over finite fields, based on a trace formula for the action of a Frobenius operator on certain spaces of p-adic analytic functions. One can consider a…

We derive a cohomological formula for the analytic index of the Dirac-Ramond operator and we exhibit its modular properties.

A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined…

We define an analogue of the Dirac operator for the degenerate affine Hecke-Clifford algebra. A main result is to relate the central characters of the degenerate affine Hecke-Clifford algebra with the central characters of the Sergeev…

Motivated by the supersymmetric version of Dirac's theory, chiral models in field theory, and the quest of a geometric fundament for the Standard Model, we describe an approach to the differential geometry of vector bundles on…

The purpose of this paper is to study generalizations of Gamma-homology in the context of operads. Good homology theories are associated to operads under appropriate cofibrancy hypotheses, but this requirement is not satisfied by usual…

This paper is a mixture of expository material and current research material. Among new results are examples of generalised harmonic spinors and their gauged version, the generalised Seiberg-Witten equations.

Let $\mathfrak{g}$ be a reductive Lie algebra over $\mathbb{C}$. For any simple weight module of $\mathfrak{g}$ with finite-dimensional weight spaces, we show that its Dirac cohomology is vanished unless it is a highest weight module. This…

The recent article "On Gromov's dihedral extremality and rigidity conjectures" by Jinmin Wang, Zhizhang Xie and Guoliang Yu makes a number of claims for self-adjoint extensions of Dirac type operators on manifolds with corners under local…

In this paper we define a new presentation for the Dunkl-Opdam subalgebra of the rational Cherednik algebra. This shows that the Dunkl-Opdam subalgebra is a Drinfeld algebra. We use this fact to define Dirac cohomology for the DO…

Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac…

We prove that for the radial Dirac equation with Coulomb-type potential the generalized dynamical scattering operator coincides with the corresponding generalized stationary scattering operator. This fact is a quantum mechanical analogue of…

As is known, the so-called Dirac $K$-operator commutes with the Dirac Hamiltonian for arbitrary central potential $V(r)$. Therefore the spectrum is degenerate with respect to two signs of its eigenvalues. This degeneracy may be described by…

A Dirac operator D on the standard Podles sphere is defined and investigated. It yields a spectral triple such that |D|^{-z} is of trace class for Re z>0. Commutators with the Dirac operator give the distinguished 2-dimensional covariant…

We prove a dichotomy of almost periodicity for reflectionless one-dimensional Dirac operators whose spectra satisfy certain geometric conditions, extending work of Volberg--Yuditskii. We also construct a weakly mixing Dirac operator with a…

In this paper we will derive an explicit description of the genuine projective representations of the symmetric group $S_n$ using Dirac cohomology and the branching graph for the irreducible genuine projective representations of $S_n$. In…