# Four families of Weyl group orbit functions of B 3 and C 3

@article{Hakova2013FourFO, title={Four families of Weyl group orbit functions of B 3 and C 3}, author={Lenka H'akov'a and Jivr'i Hrivn'ak and Jivr'i Patera}, journal={Journal of Mathematical Physics}, year={2013}, volume={54}, pages={083501-083501} }

The properties of the four families of special functions of three real variables, called here C-, S-, Ss-, and Sl-functions, are studied. The Ss- and Sl-functions are considered in all details required for their exploitation in Fourier expansions of digital data, sampled on finite fragment of lattices of any density and of the 3D symmetry imposed by the weight lattices of B3 and C3 simple Lie algebras/groups. The continuous interpolations, which are induced by the discrete expansions, are…

## 13 Citations

### Generalized discrete orbit function transforms of affine Weyl groups

- Mathematics
- 2014

The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight…

### Interpolation of Multidimensional Digital Data Using Weyl Group Orbit Functions

- Mathematics
- 2014

Orbit functions are families of special functions related to the Weyl groups of simple Lie algebras. They are complex functions depending on n variables where n is the rank of the underlying Lie…

### ON CONNECTING WEYL-ORBIT FUNCTIONS TO JACOBI POLYNOMIALS AND MULTIVARIATE (ANTI)SYMMETRIC TRIGONOMETRIC FUNCTIONS

- Mathematics
- 2016

The aim of this paper is to make an explicit link between the Weyl-orbit functions and the corresponding polynomials, on the one hand, and to several other families of special functions and…

### Dual-Root Lattice Discretization of Weyl Orbit Functions

- MathematicsJournal of Fourier Analysis and Applications
- 2019

Four types of discrete transforms of Weyl orbit functions on finite point sets are developed. The point sets are formed by intersections of dual-root lattices with fundamental domains of affine Weyl…

### Dual-Root Lattice Discretization of Weyl Orbit Functions

- MathematicsJournal of Fourier Analysis and Applications
- 2019

Four types of discrete transforms of Weyl orbit functions on finite point sets are developed. The point sets are formed by intersections of dual-root lattices with fundamental domains of affine Weyl…

### Generalized Dual-Root Lattice Transforms of Affine Weyl Groups

- MathematicsSymmetry
- 2020

The coinciding cardinality of the point and label sets and corresponding discrete orthogonality relations of Weyl orbit functions are demonstrated and the explicit counting formulas for the numbers of elements contained in the pointand label sets are calculated.

### Weight-Lattice Discretization of Weyl-Orbit Functions

- Mathematics
- 2016

Weyl-orbit functions have been defined for each simple Lie algebra, and permit Fourier-like analysis on the fundamental region of the corresponding affine Weyl group. They have also been discretized,…

### On immanant functions related to Weyl groups of An

- Mathematics
- 2014

In this work, we recall the definition of matrix immanants, a generalization of the determinant and permanent of a matrix. We use them to generalize families of symmetric and antisymmetric orbit…

### Multivariate Chebyshev polynomials and FFT-like algorithms

- Mathematics, Computer Science
- 2020

A multivariate Gauss-Jacobi procedure for the development of orthogonal transforms is proven and two theorems on fast algorithms in algebraic signal processing, one based on a decomposition property of certain polynomials and the other based on induced modules, are proven as multivariate generalizations of prior theorem.

### Families of orthogonal functions defined by the Weyl groups of compact Lie groups

- Mathematics
- 2013

Plusieurs familles de fonctions speciales de plusieurs variables, appelees fonctions d'orbites, sont definies dans le contexte des groupes de Weyl de groupes de Lie simples compacts/d'algebres de Lie…

## References

SHOWING 1-10 OF 35 REFERENCES

### New families of Weyl group orbit functions

- Mathematics
- 2012

Two families of Weyl group-invariant functions, denoted C, S, are known to arise from the irreducible representations of the compact simple Lie groups, and they have been studied extensively. These…

### Four types of special functions of G 2 and their discretization

- Mathematics
- 2012

Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G 2, are compared and described. Two of the four families (called here C- and…

### On discretization of tori of compact simple Lie groups: II

- Mathematics
- 2012

The discrete orthogonality of special function families, called C- and S-functions, which are derived from the characters of compact simple Lie groups, is described in Hrivnák and Patera (2009 J.…

### Six types of E-functions of the Lie groups O(5) and G(2)

- Mathematics
- 2012

New families of E-functions are described in the context of the compact simple Lie groups O(5) and G(2). These functions of two real variables generalize the common exponential functions and for each…

### On discretization of tori of compact simple Lie groups

- Mathematics
- 2009

Three types of numerical data are provided for simple Lie groups of any type and rank. These data are indispensable for Fourier-like expansions of multidimensional digital data into finite series of…

### E-Orbit Functions

- Mathematics
- 2008

We review and further develop the theory of E-orbit functions. They are func- tions on the Euclidean spaceEn obtained from the multivariate exponential function by sym- metrization by means of an…

### Computation of character decompositions of class functions on compact semisimple Lie groups

- Mathematics
- 1987

A new algorithm is described for splitting class functions of an arbitrary semisimple compact Lie group K into sums of irreducible characters. The method is based on the use of elements of finite…

### Discrete and continuous cosine transform generalized to Lie groups SU(3) and G(2)

- Mathematics
- 2005

In the paper we complete the development and description of the four variants of two-dimensional generalization of the cosine transform started in [Patera and Zaratsyan, J. Math Phys. 46, 053514…

### Characters of Elements of Finite Order in Lie Groups

- Mathematics, Computer Science
- 1984

An algorithm for effectively computing their character values which utilizes double coset decompositions in the Weyl group and a fast algorithm for determining weight space multiplicities which were developed earlier are introduced.

### Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group

- Mathematics
- 2006

The paper is about methods of discrete Fourier analysis in the context of Weyl group symmetry. Three families of class functions are defined on the maximal torus of each compact simply connected…