Statement of Weyl Character Formula
The character of an irreducible representation V of a compact Lie group G is given by
where
- ρ is the half the sum of the positive roots;
- W is the Weyl group;
- λ is the highest weight of the irreducible representation V;
- α runs over the positive roots of the Lie group.
- is the length of the Weyl group element, defined to be the minimal number of reflections with respect to simple roots such that equals the product of those reflections.
Read more about this topic: Weyl Character Formula
Famous quotes containing the words statement of, statement, character and/or formula:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“Most personal correspondence of today consists of letters the first half of which are given over to an indexed statement of why the writer hasn’t written before, followed by one paragraph of small talk, with the remainder devoted to reasons why it is imperative that the letter be brought to a close.”
—Robert Benchley (1889–1945)
“When needs and means become abstract in quality, abstraction is also a character of the reciprocal relation of individuals to one another. This abstract character, universality, is the character of being recognized and is the moment which makes concrete, i.e. social, the isolated and abstract needs and their ways and means of satisfaction.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
—Pierre Simon De Laplace (1749–1827)