Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Representations of the rank two Racah algebra and orthogonal multivariate polynomials

Abstract : The algebraic structure of the rank two Racah algebra is studied in detail. We provide an automorphism group of this algebra, which is isomorphic to the permutation group of five elements. This group can be geometrically interpreted as the symmetry of a folded icosidodecahedron. It allows us to study a class of equivalent irreducible representations of this Racah algebra. They can be chosen symmetric so that their transition matrices are orthogonal. We show that their entries can be expressed in terms of Racah polynomials. This construction gives an alternative proof of the recurrence, difference and orthogonal relations satisfied by the Tratnik polynomials, as well as their expressions as a product of two monovariate Racah polynomials. Our construction provides a generalization of these bivariate polynomials together with their properties.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03700687
Contributor : Virginie Malaval Connect in order to contact the contributor
Submitted on : Tuesday, June 21, 2022 - 1:12:39 PM
Last modification on : Wednesday, June 22, 2022 - 3:26:57 AM

Links full text

Identifiers

  • HAL Id : hal-03700687, version 1
  • ARXIV : 2206.01031

Citation

N. Crampe, L. Frappat, E. Ragoucy. Representations of the rank two Racah algebra and orthogonal multivariate polynomials. 2022. ⟨hal-03700687⟩

Share

Metrics

Record views

0