Bannai-Ito polynomials and dressing chains
Maxim Derevyagin, Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
TL;DR
This paper explores the relationship between Bannai-Ito polynomials, SDG maps, and dressing chains, revealing new connections within algebraic structures and polynomial theory.
Contribution
It demonstrates how Bannai-Ito polynomials and their kernel polynomials naturally emerge from the framework of SDG maps and dressing chains.
Findings
Bannai-Ito polynomials are linked to SDG maps.
Complementary Bannai-Ito polynomials arise as kernel polynomials.
New algebraic connections between polynomials and dressing chains are established.
Abstract
Schur-Delsarte-Genin (SDG) maps and Bannai-Ito polynomials are studied. SDG maps are related to dressing chains determined by quadratic algebras. The Bannai-Ito polynomials and their kernel polynomials -- the complementary Bannai-Ito polynomials -- are shown to arise in the framework of the SDG maps.
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