structure constants

structure constants

[′strək·chər ‚kän·stəns]
(mathematics)
A set of numbers that serve as coefficients in expressing the commutators of the elements of a Lie algebra.
References in periodicals archive ?
It is also worth mentioning that in [3] Buch obtained the Littlewood-Richardson rule for the structure constants of Grothendieck polynomials [G.sub.[lambda]](x), and hence the Schubert structure constants of the K-theory of Grassmannians (see also the paper [9] by Ikeda-Shimazaki for another proof) For the equivariant K-theory of Grassmannians (or equivalently for [G.sub.[lambda]](x|b)), the structure constants were determined by Pechenik and Yong in [20] by introducing a new combinatorial object called genomic tableaux.
Lie algebras come with a skew-symmetric product called a Lie bracket and can be characterized by the so-called structure constants with respect to some basis of the linear space.
where [f.sup.(a).sub.(b)(c)] are the real structure constants of the gauge group and
Developments in algebraic geometry and topology convert the problem into the computation of intersection numbers of certain subvarieties in the Grassmannian, which in turn is encoded by the structure constants of Schubert classes [{[[sigma].sub.[lambda]]}.sub.[lambda][subset]rect] for the cohomology ring of the Grassmannian Gr(a, n).
On the two decimals rounded energy of the two-sided distribution can be calculated with the help of equations (6) and (9) knowing the CODATA value of the energy equivalent of the mass of the electron [E.sub.e] = 510998.91 eV, and the appropriate distributed inverse fine structure constants [[alpha].sup.-1.sub.0-sided] = 137.036006 and [[alpha].sup.-1.sub.2-sided] = 137.036014 [1]:
In this note we deal with algebras where the number of anticommuting generators is arbitrary and give the general form of the structure constants. These superalgebras are definitely interesting from mathematical point of view.
VALLEE, Continued fraction algorithms, functional operators, and structure constants, Theoretical Computer Science, 194, (1998), 1-34.
These estimated values included g-factors, hyperfine structure constants, and line widths that characterized the shape and intensity of each spectral component.
The derived molecular properties, such as rotational and centrifugal distortion constants, hyperfine structure constants, electric dipole moments, rotational g-factors and internuclear distances (for diatomic molecules) are listed with one standard deviation uncertainties for all species.
On the other hand Giambelli's formula provides explicit structure constants and is surprisingly simple and uniform across Lie types.
Schubert polynomials are known to multiply positively since their structure constants enumerate flags in suitable triple intersections of Schubert varieties.
Let [C.sup.[bar.v].sub.[bar.[lambda]],[bar.[mu]]] (G/P) denote the Schubert structure constants for G/P, i.e.,

Full browser ?