Results 61 to 70 of about 2,972 (226)

On conjugating representations and adjoint representations of semisimple groups

Inventiones Mathematicae, 1988
Let G be a reductive algebraic group over an algebraically closed field k and let G act (as k-algebra automorphisms) on a finitely generated k- algebra A. Suppose the algebra of invariants, \(C=A\) G, is a free polynomial k-algebra and that A is flat as a C-module.
openaire   +1 more source

Reconfigurable Giant Nonreciprocity at Near‐Normal Incidence via Phase‐Change Magneto‐Optical Metagratings

Laser &Photonics Reviews, EarlyView.
A phase‐change magneto‐optical metagrating combines GST switching with InAs guided‐mode resonances to achieve strong nonreciprocal absorption contrast near normal incidence. A static magnetic bias creates direction‐dependent resonant splitting, while GST crystallization quenches and latches the response.
Ye Ming Qing, Yi Shen, Jun Wu, Shunsuke Murai, Zhaogang Dong, Koichi Okamoto   +5 more
wiley   +1 more source

Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14

Mathematische Nachrichten, EarlyView.
ABSTRACT The isometry between the type IV6 and the type II4 hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8‐folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces
Flora Poon
wiley   +1 more source

On the Stiefel-Whitney classes of the adjoint representation of $E_8$

Kyoto Journal of Mathematics, 2004
Let \(\widetilde{E_8}\) be the \(3\)-connected covering space of the simply connected Lie group \(E_8\). Let \(\pi_8: \widetilde{E_8} \to E_8\) be the covering map and \(\pi_8^*: H^*(Be_8) \to H^*(B\widetilde{E_8})\) be the induced map between the \(\mathbb{Z}_2\) cohomology of the classifying spaces.
openaire   +4 more sources

Exterior powers of the adjoint representation and the Weyl ring of E8 [PDF]

Journal of Algebra, 2020
I derive explicitly all polynomial relations in the character ring of $E_8$ of the form $χ_{\wedge^k \mathfrak{e}_8} - \mathfrak{p}_{k} (χ_{1}, \dots, χ_{8})=0$, where $\wedge^k \mathfrak{e}_8$ is an arbitrary exterior power of the adjoint representation and $χ_{i}$ is the $i^{\rm th}$ fundamental character.
openaire   +4 more sources

Investigating Tuberculosis Dynamics Under Various Control Strategies: A Comprehensive Analysis Using Real Statistical Data

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In the present investigation, a mathematical model with vaccination, treatment, and environmental impact under real data is presented. Initially, we present the model without any interventions, followed by an examination of its equilibrium points.
Bashir Al‐Hdaibat, Mahmoud H. DarAssi, Irfan Ahmad, Muhammad Altaf Khan, Reem Algethamie   +4 more
wiley   +1 more source

On different approaches to IRF lattice models. Part II

Journal of High Energy Physics
This paper represents a continuation of our previous work, where the Boltzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories.
Vladimir Belavin, Doron Gepner, J. Ramos Cabezas, Boris Runov   +3 more
doaj   +1 more source

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling [PDF]

Hydrology and Earth System Sciences
Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and ...
Y. Song, W. J. M. Knoben, M. P. Clark, D. Feng, D. Feng, K. Lawson, K. Sawadekar, C. Shen   +7 more
doaj   +1 more source

On the depth of the adjoint representations

Let $F$ be a non-archimedean local field of odd residual characteristic $p$. The depth of a smooth representation of ${\rm GL}_n(F)$ is an invariant of Local Langlands Correspondence (LLC). The analogous notion on the Galois side of LLC is known as the slope of a local Galois representation.
Jana, Arindam, Mondal, Amiya
openaire   +2 more sources

Adjoint Representations of the Symmetric Group

, 2018
We study the restriction to the symmetric group, $\mc{S}_n$ of the adjoint representation of $\mt{GL}_n(\C)$. We determine the irreducible constituents of the space of symmetric as well as the space of skew-symmetric $n\times n$ matrices as $\mc{S}_n$-modules.
Can, Mahir Bilen, Jones, Miles
openaire   +2 more sources