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A central conjecture in inverse Galois theory, proposed by D\`{e}bes and Deschamps, asserts that every finite split embedding problem over an arbitrary field can be regularly solved. We give an unconditional proof of a consequence of this…
We apply the Faddeev-Jackiw method to the Hamiltonian analysis of the massless spin-two field. As expected, the reduced Hamiltonian contains only the traceless-transverse tensor, while some, but not all of the non-propagating components are…
Let $K/F$ be a quadratic extension of $p$-adic fields, $\sigma$ the nontrivial element of the Galois group of $K$ over $F$, and $\pi$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $\pi^{\vee}$ the smooth contragredient…
We use enhanced Langlands parameters to obtain a classification for irreducible representations of twisted $p$-adic general linear groups in unramified principal series. We give the definition of standard representations and prove the…
This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is…
We aim to analyze the consistency of the deformation of the Heisenberg algebra in the setting of constrained Hamiltonian systems, providing a procedure to induce the deformation on the Poisson algebra after symplectic reduction. We…
The HLE theorem is proven for effective Lagrangians with arbitrary interactions of scalars, fermions, massless and massive vector bosons. This theorem states that the correct Hamiltonian path intergral formalism is equivalent to the…
Microscopically conserving reduced models of many-body systems have a long, highly successful history. Established theories of this type are the random-phase approximation for Coulomb fluids and the particle-particle ladder model for…
A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of…
We prove that the two-dimensional Gaussian Free Field describes the asymptotics of global fluctuations of a multilevel extension of the general beta Jacobi random matrix ensembles. Our approach is based on the connection of the Jacobi…
We present the general framework of \'Ecalle's moulds in the case of linearization of a formal vector field without and within resonances. We enlighten the power of moulds by their universality, and calculability. We modify then \'Ecalle's…
We show that Joseph-Lamprou's path model for representations of generalized Kac-Moody algebras can be embedded into Littelmann's path model for certain Kac-Moody algebras. Using this embedding, for Joseph-Lamprou's path crystals, we give a…
The Hamiltonian reduction of the massless spin-two field theory is carried out following the Faddeev-Jackiw approach. The reduced Hamiltonian contains only the traceless-transverse fields, but not all of the non-propagating components can…
Several refinements are made in a theory which starts with a Planck-scale statistical picture and ends with supersymmetry and a coupling of fundamental fermions and bosons to SO(N) gauge fields. In particular, more satisfactory treatments…
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and…
I investigate the Poisson-sigma model on the classical and quantum level. First I show how the interaction can be obtained by a deformation of the classical master equation of an Abelian BF theory in two dimensions. On the classical level…
We show that any Lambda-ring, in the sense of Riemann-Roch theory, which is finite etale over the rational numbers and has an integral model as a Lambda-ring is contained in a product of cyclotomic fields. In fact, we show that the category…
This work deals with several aspects of the extension to Abelian Higgs models of the deformation method originally developed for scalar field models. We present several examples allowing to transform self-dual solutions of different…
The transformation properties of a Kalb-Ramond field are those of a gauge potential. However, it is not clear what is the group structure to which these transformations are associated. In this paper, we complete a program started in…
We study a solenoidal-potential type decomposition of a symmetric $m$-tensor field in $\Rb^2$, and its implications to injectivity questions for the momentum and elastic ray transforms. For symmetric tensor fields, a general decomposition…