TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.6.5.054
TI  - Elliptic deformation of $\mathcal{W}_N$-algebras
PY  - 2019/05/07
UR  - https://scipost.org/SciPostPhys.6.5.054
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 6
IS  - 5
SP  - 054
A1  - Avan, Jean
AU  - Frappat, Luc
AU  - Ragoucy, Eric
AB  - We construct $q$-deformations of quantum $\mathcal{W}_N$ algebras with elliptic structure functions. Their spin $k+1$ generators are built from $2k$ products of the Lax matrix generators of ${\mathcal{A}_{q,p}(\widehat{gl}(N)_c)}$). The closure of the algebras is insured by a critical surface condition relating the parameters $p,q$ and the central charge $c$. Further abelianity conditions are determined, either as $c=-N$ or as a second condition on $p,q,c$. When abelianity is achieved, a Poisson bracket can be defined, that we determine explicitly. One connects these structures with previously built classical $q$-deformed $\mathcal{W}_N$ algebras and quantum $\mathcal{W}_{q,p}(\mathfrak{sl}_N)$.
ER  -

@Article{10.21468/SciPostPhys.6.5.054,
	title={{Elliptic deformation of $\mathcal{W}_N$-algebras}},
	author={Jean Avan and Luc Frappat and Eric Ragoucy},
	journal={SciPost Phys.},
	volume={6},
	pages={054},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.6.5.054},
	url={https://scipost.org/10.21468/SciPostPhys.6.5.054},
}