# Quadratic relations of the deformed W-superalgebra Wq,t(sl(2|1))

@article{Kojima2019QuadraticRO,
title={Quadratic relations of the deformed W-superalgebra Wq,t(sl(2|1))},
author={Takeo Kojima},
journal={arXiv: Quantum Algebra},
year={2019}
}
• T. Kojima
• Published 5 December 2019
• Mathematics
• arXiv: Quantum Algebra
This paper is a continuation of study by J.Ding and B.Feigin. We find a bosonization of the deformed $W$-superalgebras ${\cal W}_{q t}(\mathfrak{sl}(2|1))$ that commutes up-to total difference with deformed screening currents. Using our bosonization, we derive a set of quadratic relations of generators of the deformed $W$-superalgebra ${\cal W}_{q t}(\mathfrak{sl}(2|1))$. The deformed $W$-superalgebra is independent of the choice of a Dynkin-diagram for the superalgebra $\mathfrak{sl}(2|1… 7 Citations The quantum toroidal algebra of$gl_1$provides many deformed W-algebras associated with (super) Lie algebras of type A. The recent work by Gaiotto and Rapcak suggests that a wider class of deformed • Go Noshita • Mathematics Journal of High Energy Physics • 2022 Abstract We discuss the 5d AGT correspondence of supergroup gauge theories with A-type supergroups. We introduce two intertwiners called positive and negative intertwiners to compute the instanton • Mathematics Journal of High Energy Physics • 2022 Recently, new classes of infinite-dimensional algebras, quiver Yangian (QY) and shifted QY, were introduced, and they act on BPS states for non-compact toric Calabi-Yau threefolds. In particular, • T. Kojima • Mathematics Symmetry, Integrability and Geometry: Methods and Applications • 2022 . We revisit the free ﬁeld construction of the deformed W -algebra by Frenkel and Reshetikhin, Commun. Math. Phys. 197 , 1-31 (1998), where the basic W -current has been identiﬁed. Herein, we • Mathematics Journal of High Energy Physics • 2022 Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian gl\documentclass[12pt]{minimal} \usepackage{amsmath} • Mathematics • 2021 We revisit the free field construction of the deformed W -algebra by Frenkel and Reshetikhin, Commun. Math. Phys. 197, 1-31 (1998), where the basic W -current has been identified. Herein, we We find the free field construction of the basic W-current and screening currents for the deformed W-superalgebra Wq,tA(M,N) associated with Lie superalgebra of type A(M, N). Using this free field ## References SHOWING 1-10 OF 49 REFERENCES We obtain an explicit expression for the defining relation of the deformed WN algebra,${\rm DWA}(\widehat{\mathfrak{sl}}_N)_{q,t}$. Using this expression we can show that, in the q→1 limit,${\rm
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Let [Formula: see text] be a finite-dimensional vector space over a field [Formula: see text] of characteristic zero, [Formula: see text] an anti-commutative product on [Formula: see text] and