Weyl Group Orbit Functions in Image Processing

2015 ◽  
pp. 189-194
Author(s):  
Goce Chadzitaskos ◽  
Lenka Háková ◽  
Ondřej Kajínek
Keyword(s):  
Image Processing ◽  
Weyl Group ◽  
Group Orbit

scholarly journals Weyl Group Orbit Functions in Image Processing

2014 ◽  
Vol 05 (03) ◽  
pp. 501-511 ◽  
Author(s):  
Goce Chadzitaskos ◽  
Lenka Háková ◽  
Ondřej Kajínek
Keyword(s):  
Image Processing ◽  
Weyl Group ◽  
Group Orbit

scholarly journals ON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS

2016 ◽  
Vol 56 (3) ◽  
pp. 202 ◽  
Author(s):  
Lenka Háková ◽  
Jiří Hrivnák ◽  
Lenka Motlochová
Keyword(s):  
Weyl Group ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Jacobi Polynomials ◽  
Special Functions ◽  
Root Systems ◽  
Full Generality ◽  
Cubature Formulas ◽  
Special Cases ◽  
Group Orbit

The aim of this article is to describe several cubature formulas related to the Weyl group orbit functions, i.e. to the special cases of the Jacobi polynomials associated to root systems. The diagram containing the relations among the special functions associated to the Weyl group orbit functions is presented and the link between the Weyl group orbit functions and the Jacobi polynomials is explicitly derived in full generality. The four cubature rules corresponding to these polynomials are summarized for all simple Lie algebras and their properties simultaneously tested on model functions. The Clenshaw-Curtis method is used to obtain additional formulas connected with the simple Lie algebra <em>C</em><sub>2</sub>.

scholarly journals ON GENERALIZATION OF SPECIAL FUNCTIONS RELATED TO WEYL GROUPS

2016 ◽  
Vol 56 (6) ◽  
pp. 440-447
Author(s):  
Lenka Háková ◽  
Agnieszka Tereszkiewicz
Keyword(s):  
Weyl Group ◽  
Lie Algebras ◽  
Special Functions ◽  
Irreducible Representations ◽  
Weyl Groups ◽  
One Dimensional ◽  
Complex Functions ◽  
Group Orbit ◽  
Rank 2 ◽  
Definition Of

Weyl group orbit functions are defined in the context of Weyl groups of simple Lie algebras. They are multivariable complex functions possessing remarkable properties such as (anti)invariance with respect to the corresponding Weyl group, continuous and discrete orthogonality. A crucial tool in their definition are so-called sign homomorphisms, which coincide with one-dimensional irreducible representations. In this work we generalize the definition of orbit functions using characters of irreducible representations of higher dimensions. We describe their properties and give examples for Weyl groups of rank 2 and 3.

scholarly journals THE CONSTRUCTION OF TRIGONOMETRIC INVARIANTS FOR WEYL GROUPS AND THE DERIVATION OF THE CORRESPONDING EXACTLY SOLVABLE SUTHERLAND MODELS

1999 ◽  
Vol 14 (14) ◽  
pp. 937-949 ◽  
Author(s):  
O. HASCHKE ◽  
W. RÜHL
Keyword(s):  
Weyl Group ◽  
Polynomial Algebra ◽  
Solvable Model ◽  
Weyl Groups ◽  
Root Lattice ◽  
Root Space ◽  
Exactly Solvable Model ◽  
Exactly Solvable ◽  
Group Orbit

Trigonometric invariants are defined for each Weyl group orbit on the root lattice. They are real and periodic on the co-root lattice. Their polynomial algebra is spanned by a basis which is calculated by means of an algorithm. The invariants of the basis can be used as coordinates in any cell of the co-root space and lead to an exactly solvable model of Sutherland type. We apply this construction to the F4 case.

scholarly journals Four families of Weyl group orbit functions ofB3andC3

2013 ◽  
Vol 54 (8) ◽  
pp. 083501 ◽  
Author(s):  
Lenka Háková ◽  
Jiří Hrivnák ◽  
Jiří Patera
Keyword(s):  
Weyl Group ◽  
Group Orbit

scholarly journals Characteristic cycles and the microlocal geometry of the Gauss map, II

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas Krämer
Keyword(s):  
Weak Solution ◽  
Weyl Group ◽  
Lie Algebras ◽  
Abelian Variety ◽  
Cotangent Bundle ◽  
Abelian Varieties ◽  
Gauss Map ◽  
Schottky Problem ◽  
Group Orbit

Abstract We show that any Weyl group orbit of weights for the Tannakian group of semisimple holonomic 𝒟 {{\mathscr{D}}} -modules on an abelian variety is realized by a Lagrangian cycle on the cotangent bundle. As applications we discuss a weak solution to the Schottky problem in genus five, an obstruction for the existence of summands of subvarieties on abelian varieties, and a criterion for the simplicity of the arising Lie algebras.

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