Results 241 to 250 of about 139,367 (266)

Inverse design of nonlinear metasurfaces for sum frequency generation. [PDF]

Nanophotonics
Li N, Zhang J, Neshev DN, Sukhorukov AA.
europepmc   +1 more source

Exploring AI in metasurface structures with forward and inverse design. [PDF]

iScience
Yang G, Xiao Q, Zhang Z, Yu Z, Wang X, Lu Q.   +5 more
europepmc   +1 more source

The adjoint representation in rings of functions [PDF]

Representation Theory of the American Mathematical Society, 1997
Let G G be a connected, simple Lie group of rank n n defined over the complex numbers. To a parabolic subgroup P P in G G of semisimple rank r r , one can associate n − r n-r positive integers coming from the theory of ...
Peter E. Trapa, Eric Sommers
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Adjoint Representations and the Derivative of exp [PDF]

, 2020
In this chapter, in preparation for defining the Lie bracket on the Lie algebra of a Lie group, we introduce the adjoint representations of the group \(\mathbf {GL}(n, {\mathbb {R}})\) and of the Lie algebra \({\mathfrak {gl}}(n, {\mathbb {R}})\). The map \(\mathrm {Ad}\colon \mathbf {GL}(n, {\mathbb {R}})\rightarrow \mathbf {GL}({\mathfrak {gl}}(n ...
Jocelyn Quaintance, Jean Gallier
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Exterior Powers of the Adjoint Representation

Canadian Journal of Mathematics, 1997
AbstractExterior powers of the adjoint representation of a complex semisimple Lie algebra are decomposed into irreducible representations, to varying degrees of satisfaction.
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Adjoint representations of exceptional Lie algebras

Theoretical and Mathematical Physics, 1987
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. A. Ol'shanetskii, V. B. K. Rogov
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The Adjoint Representation and the Adjoint Action

2002
The purpose of this article is to study in detail the actions of a semisimple Lie or algebraic group on its Lie algebra by the adjoint representation and on itself by the adjoint action. We will focus primarily on orbits through nilpotent elements in the Lie algebra; these are called nilpotent orbits for short.
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A homotopy construction of the adjoint representation for Lie groups [PDF]

Mathematical Proceedings of the Cambridge Philosophical Society, 2002
Let G be a compact, simply-connected, simple Lie group and T ⊂ G a maximal torus. The purpose of this paper is to study the connection between various fibrations over BG (where G is a compact, simply-connected, simple Lie group) associated to the adjoint representation and homotopy colimits over poset categories [Cscr ], hocolim[Cscr ]BGI where
Nitu Kitchloo, Natàlia Castellana
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