• Corpus ID: 221686445

Quadratic relations of the deformed W-superalgebra

@inproceedings{Kojima2020QuadraticRO,
  title={Quadratic relations of the deformed W-superalgebra},
  author={Takeo Kojima},
  year={2020}
}
This paper is a continuation of the study by Ding and Feigin, Contemp.Math. 248, 83 (1998). We find a bosonization of the deformed W -superalgebras Wq,t(sl(2|1)) that commute up to the total difference with deformed screening currents. Using the bosonization, we derive a set of quadratic relations of generators for the deformed W -superalgebra Wq,t(sl(2|1)), which is independent of the choice of Dynkin-diagram for the superalgebra sl(2|1), though the deformed screening currents depend on it. 

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References

SHOWING 1-10 OF 40 REFERENCES

Deformations of W-algebras associated to simple Lie algebras

Deformed W-algebra Wq,t(g) associated to an arbitrary simple Lie alge- bra g is defined together with its free field realizations and the screening operators. Explicit formulas are given for

Drinfeld–Sokolov Reduction for Difference Operators and Deformations of W-Algebras¶ II. The General Semisimple Case

Abstract:The paper is the sequel to [9]. We extend the Drinfeld--Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic

Integrals of motion from quantum toroidal algebras

We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi,

Deformed Virasoro Algebras from Elliptic Quantum Algebras

We revisit the construction of deformed Virasoro algebras from elliptic quantum algebras of vertex type, generalizing the bilinear trace procedure proposed in the 1990s. It allows us to make contact

Commutation relations of vertex operators for Uq(sl^(M|N))

  • T. Kojima
  • Mathematics
    Journal of Mathematical Physics
  • 2018
We consider commutation relations and invertibility relations of vertex operators for the quantum affine superalgebra $U_q(\widehat{sl}(M|N))$ by using bosonization. We show that vertex operators

Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators

Starting from bosonization, we study the operator that commute or commute up-to a total difference with of any quantized screen operator of a free field. We show that if there exists a operator in

Drinfeld–Sokolov Reduction for Difference Operators and Deformations of -Algebras¶I. The Case of Virasoro Algebra

Abstract:We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical -algebras by reduction from Poisson-Lie loop groups. We consider in

Integrals of motion and quantum groups

A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohomology classes of

On the defining relations of the affine Lie superalgebras and their quantized universal enveloping superalgebras

In this paper, we give defining relations of the affine Lie superalgebras an and defining relations of a super-version of the Drinfeld[D]-Jimbo[J] affine quantized universal enveloping algebras. As a

A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions

A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra.