In mathematics, the Weyl integration formula, introduced by Hermann Weyl, is an integration formula for a compact connected Lie group G in terms of a...

In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms...

In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions...

In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not...

MathWorld. Weisstein, Eric W. "Weyl's Criterion". MathWorld. Weyl's Criterion at PlanetMath. Lecture notes by Charles Walkden with proof of Weyl's Criterion...

Length of a Weyl group element Restricted Weyl group Weyl integral Weyl integration formula Weyl law Weyl metrics Weyl module Weyl notation Weyl quantization...

Majorana–Weyl spinor Peter–Weyl theorem Schur–Weyl duality Weyl algebra Weyl basis of the gamma matrices Weyl chamber Weyl character formula Weyl equation...

introduced by Adolf Hurwitz (1897) for the special linear group and by Hermann Weyl for general semisimple groups. It applies to show that the representation...

algebra, the Weyl algebras are abstracted from the ring of differential operators with polynomial coefficients. They are named after Hermann Weyl, who introduced...

José Enrique Moyal; also called the star product or Weyl–Groenewold product, after Hermann Weyl and Hilbrand J. Groenewold) is an example of a phase-space...

elements—forms an orthonormal set in the space of square integrable class functions. But by the Weyl character formula, the characters of the irreducible representations...

streamline Weyl's method. Kodaira also generalised Weyl's method to singular ordinary differential equations of even order and obtained a simple formula for...

formula without additional domain assumptions. Indeed, there exist operators satisfying the canonical commutation relation but not the Weyl relations...

complex semisimple Lie algebra in terms of highest weights. 3.  The Weyl integration formula says: given a compact connected Lie group G with a maximal torus...

the Weyl group of M. Langlands (1983) suggested the possibility a stable refinement of the trace formula that can be used to compare the trace formula for...

was worked out mainly by E. Cartan and H. Weyl and because of that, the theory is also known as the Cartan–Weyl theory. The theory gives the structural...

Hermann Weyl in 1927, in a context related to representation theory in mathematics (see Weyl quantization). In effect, it is the Wigner–Weyl transform...

standard explanation of this in one-variable integration theory is that, when the limits of integration are in the opposite order (b < a), the increment...

singularities via Dirichlet's principle. In Weyl's method of orthogonal projection, Lebesgue's theory of integration had been used to realise Hilbert spaces...

The definition is due to Hermann Weyl (1917). Sobolev space Lizorkin, P.I. (2001) [1994], "Fractional integration and differentiation", Encyclopedia...

the most often used. It is a generalization of the Cauchy formula for repeated integration to arbitrary order. Here, n = ⌈ q ⌉ {\displaystyle n=\lceil...

trivial for a contractible region, for k > 0. For smooth manifolds, integration of forms gives a natural homomorphism from the de Rham cohomology to...

the archetypal example, one may well consider Groenewold's original "Moyal–Weyl" ⋆ {\displaystyle \star } -product. A Kontsevich graph is a simple directed...

k ] = 0. {\displaystyle C_{[ijk]}=0.\,} In addition the Bianchi formula for the Weyl tensor can be rewritten as δ W = ( 3 − n ) C , {\displaystyle \delta...

mathematician Sophus Lie (/liː/ LEE) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres...

representation theory. He co-discovered Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the...

Harish-Chandra went on to prove an analogue for these representations of the Weyl character formula. In the case where G is not compact, the representations have infinite...

Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory...

where W is the Weyl group W = N U ( T ) / T {\displaystyle W=N_{U}(T)/T} and δ(eX) is given by a product formula (Weyl's denominator formula) which extends...

coordinate system - Integration and differentiation in spherical coordinates Stereographic projection - Properties. The Riemann's formula Kuiper, N. H. (1949)...