Higher Order Relations for ADE-Type Generalized q-Onsager Algebras
| Autor: | Pascal Baseilhac, Thu Thuy Vu |
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| Rok vydání: | 2015 |
| Předmět: |
Physics
Monomial 010308 nuclear & particles physics 010102 general mathematics Order (ring theory) Statistical and Nonlinear Physics Rank (differential topology) Type (model theory) 01 natural sciences Affine Lie algebra Combinatorics Integer 0103 physical sciences 0101 mathematics Algebra over a field Mathematical Physics |
| Zdroj: | Letters in Mathematical Physics. 105:1275-1288 |
| ISSN: | 1573-0530 0377-9017 |
| DOI: | 10.1007/s11005-015-0778-6 |
| Popis: | Let $${\left\{\mathsf{A}_j|j=0,1,\ldots,rank(g)\right\}}$$ be the fundamental generators of the generalized q-Onsager algebra $${{\cal O}_{q}({\widehat{g}})}$$ introduced in Baseilhac and Belliard (Lett Math Phys 93:213–228, 2010), where $${\widehat{g}}$$ is a simply laced affine Lie algebra. New relations between certain monomials of the fundamental generators—indexed by the integer $${r\in\mathbb{Z}^{+}}$$ —are conjectured. These relations can be seen as deformed analogs of Lusztig’s rth higher order q-Serre relations associated with $${{\cal U}_q({\widehat g})}$$ , which are recovered as special cases. The relations are proven for $${r\leq 5}$$ . For r generic, several supporting evidences are presented. |
| Databáze: | OpenAIRE |
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