Let $\mathbb F$ be a finite field. Consider direct sum $V$ of an infinite number copies F$, consider the dual space $V^\diamond$, i.~e., product F$. ${\mathbb V}=V\oplus V^\diamond$. The object paper is group $\mathbf{GL}$ continuous linear operators in V$. We reduce theory unitary representations to projective certain category whose morphisms are relations finite-dimensional spaces over In fac...

We study mirror symmetry of families elliptic K3 surfaces with fibers type $E_6,~E_7$ and $E_8$. consider a moduli space $\mathsf{T}$ the enhanced choice differential forms. show that coordinates on are given by ring quasi modular forms in two variables, groups adapted to fiber type. furthermore introduce an algebraic group $\mathsf{G}$ which acts from right construct its Lie algebra $\mathrm{L...

Abstract Let ? be a proper open cone in real Banach space V . We show that the tube domain V ? i ? ? {V\oplus i\Omega} over is biholomorphic to bounded symmetric if and only normal linearly homogeneous Finsler cone, which equiva...

Disks of low-mass bodies scattered by giant planets to large semi-major axis and constant periapsis orbits are vulnerable a buckling instability. This instability exponentially grows orbital inclinations, raises distances, coherently tilts resulting in clustering arguments periapsis. The dynamically hot system is then susceptible the formation lopsided mode. Here we show that timescale decrease...

Abstract We present a validation of long-period ( 91.68278 − 0.00041 + 0.00032 days) transiting sub-Neptune planet, TOI-1221 b ...

Abstract We report the confirmation of a TESS-discovered transiting super-Earth planet orbiting mid-G star, HD 307842 (TOI-784). The has period 2.8 days, and radial velocity (RV) measurements constrain mass to be 9.67 ...

We study the category of Sp-equivariant modules over infinite variable polynomial ring, where Sp denotes symplectic group. establish a number results about this category: for instance, we show that every finitely generated module M fits into an exact triangle $T \to F \to$ T is finite length complex torsion and "free" modules; determine Grothendieck group; (partially) structure injective module...

Patterns of symmetry breaking induced by potentials at the boundary free $O(N)$ models in $d=3- \epsilon$ dimensions are studied. We show that spontaneous these theories leads to a RG flow ending with $N - 1$ Neumann modes IR. The possibility fluctuation-induced is examined and we derive general formula for computing one-loop effective boundary. Using $\epsilon-$expansion test ideas an $O(N)\op...

The quantum Rabi model (QRM) is widely recognized as an important in systems, particularly optics. Hamiltonian $H_{\text{Rabi}}$ known to have a parity decomposition $H_{\text{Rabi}} = H_{+} \oplus H_{-}$. In this paper, we give the explicit formulas for propagator of Schr\"odinger equation (integral kernel time evolution operator) and $H_{\pm}$ by Wick rotation (meromorphic continuation) corre...