منابع مشابه
Orbit Functions of Compact Semisimple Lie Groups as Special Functions
An orbit function is the contribution to an irreducible character of a compact semisimple Lie group G of rank n from one of its Weyl group orbits. Properties of such functions will be described for compact simple Lie groups of all types. In particular, products of the functions decompose into their sums, the functions are periodic on copies of the fundamental region F of G, they are solutions o...
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We deal with the Fourier-like analysis of functions on discrete grids in two-dimensional simplexes using C− and E− Weyl group orbit functions. For these cases we present the convolution theorem. We provide an example of application of image processing using the C− functions and the convolutions for spatial filtering of the treated image.
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We decompose the ring of regular functions on the unique coadjoint orbit for complex E8 of dimension 128, finding that every irreducible representation appears exactly once. This confirms a conjecture of McGovern. We also study the unique real form of this orbit.
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For finite Lie algebras, it is shown that characters can be defined first for Weyl orbits and then for irreducible representations. For AN Lie algebras, weight multiplicities can then be calculated by only stating that characters are equivalent to Schur functions. This also means that to calculate characters there is no need to sum over Weyl groups. The compatibility with the Weyl character for...
متن کاملOrbit functions of SU(n) and Chebyshev polynomials
Orbit functions of a simple Lie group/Lie algebra L consist of exponential functions summed up over the Weyl group of L. They are labeled by the highest weights of irreducible finite dimensional representations of L. They are of three types: C-, Sand E-functions. Orbit functions of the Lie algebras An, or equivalently, of the Lie group SU(n+1), are considered. First, orbit functions in two diff...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2006
ISSN: 1815-0659
DOI: 10.3842/sigma.2006.006