Antisymmetric Orbit Functions

Antisymmetric Functions and Applications

Minimum uncertainty for antisymmetric wave functions

We study how the entropic uncertainty relation for position and momentum conjugate variables is minimized in the subspace of one-dimensional antisymmetric wave functions. Based partially on numerical evidence and partially on analytical results, a conjecture is presented for the sharp bound and for the minimizers. Conjectures are also presented for the corresponding sharp Hausdorff-Young inequa...

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...

Weyl group orbit functions in image processing

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.

Functions on the Model Orbit in E8

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.