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On Abelianity Lines in Elliptic $W$-Algebras
Jean Avana, Luc Frappatb, Eric Ragoucyb a Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS, F-95302 Cergy-Pontoise, France
b Laboratoire d'Annecy-le-Vieux de Physique Théorique LAPTh, Université Grenoble Alpes, USMB, CNRS, F-74000 Annecy, France
Abstract:
We present a systematic derivation of the abelianity conditions for the $q$-deformed $W$-algebras constructed from the elliptic quantum algebra $\mathcal{A}_{q,p}\big(\widehat{\mathfrak{gl}}(N)_{c}\big)$. We identify two sets of conditions on a given critical surface yielding abelianity lines in the moduli space ($p, q, c$). Each line is identified as an intersection of a countable number of critical surfaces obeying diophantine consistency conditions. The corresponding Poisson brackets structures are then computed for which some universal features are described.
Keywords:
elliptic quantum algebras, $W$-algebras.
Received: May 8, 2020; in final form September 22, 2020; Published online September 30, 2020
Citation:
Jean Avan, Luc Frappat, Eric Ragoucy, “On Abelianity Lines in Elliptic $W$-Algebras”, SIGMA, 16 (2020), 094, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1631 https://www.mathnet.ru/eng/sigma/v16/p94
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