The Drinfeld realization of the elliptic quantum group Bq,λ(A2(2))

@article{Kojima2004TheDR,
  title={The Drinfeld realization of the elliptic quantum group Bq,$\lambda$(A2(2))},
  author={Takeo Kojima and Hitoshi Konno},
  journal={Journal of Mathematical Physics},
  year={2004},
  volume={45},
  pages={3146-3179}
}
  • T. KojimaH. Konno
  • Published 7 January 2004
  • Mathematics
  • Journal of Mathematical Physics
We construct a realization of the L-operator satisfying the RLL-relation of the face-type elliptic quantum group Bq,λ(A2(2)). The construction is based on the elliptic analog of the Drinfeld currents of Uq(A2(2)), which forms the elliptic algebra Uq,p(A2(2)). We give a realization of the elliptic currents E(z), F(z), and K(z) as a tensor product of the Drinfeld currents of Uq(A2(2)) and a Heisenberg algebra. In the level-one representation, we also give a free field realization of the elliptic… 
3 Citations

Elliptic Quantum Toroidal Algebra $U_{q,t,p}(gl_{1,tor})$ and Affine Quiver Gauge Theories

We introduce the elliptic quantum toroidal algebra Uq,t,p(gl1,tor). Various representations in the quantum toroidal algebra Uq,t(gl1,tor) are extended to the elliptic case including the level (0,0)

Elliptic Quantum Groups U_q,p(gl_N) and E_q,p(gl_N)

We reformurate a central extension of Felder's elliptic quantum group in the FRST formulation as a topological algebra E_{q,p}(gl_N) over the ring of formal power series in p. We then discuss the

Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(A2(2))

We implement the Bethe ansatz method for the elliptic quantum group Eτ,η(A2(2)). The Bethe creation operators are constructed as polynomials of the Lax matrix elements expressed through a recurrence

Algebraic Bethe ansatz for the elliptic quantum group Etau,e(A2(2))

We implement the Bethe ansatz method for the elliptic quantum group E , A2 2 . The Bethe creation operators are constructed as polynomials of the Lax matrix elements expressed through a recurrence

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

The $q$-Wakimoto Realization of the Superalgebras $U_q(\hat{sl}(N|1))$ and $U_{q,p}(\hat{{sl}}(N|1))$

We give bosonizations of the superalgebras $U_q(\hat{sl}(N|1))$ and $U_{q,p}(\hat{sl}(N|1))$ for an arbitrary level $k \in {\bf C}$. We introduce the submodule by the $\xi$-$\eta$ system, that we

Elliptic deformed superalgebra

We introduce the elliptic superalgebra as one parameter deformation of the quantum superalgebra . For an arbitrary level k ≠ 1, we give the bosonization of the elliptic superalgebra and the screening

References

SHOWING 1-10 OF 35 REFERENCES

The elliptic algebra Uq, p(slN) and the Drinfeld realization of the elliptic quantum group Bq, λ(slN)

By using the elliptic analogue of the Drinfeld currents in the elliptic algebra U q,p (sl N ), we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic

The Elliptic Algebra and the Drinfeld Realization of the Elliptic Quantum Group

AbstractBy using the elliptic analogue of the Drinfeld currents in the elliptic algebra , we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum

K-6 DPSU-982 Elliptic algebra U q , p ( ŝl 2 ) : Drinfeld currents and vertex operators

We investigate the structure of the elliptic algebra Uq,p(ŝl2) introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum affine algebra

Quasi-Hopf twistors for elliptic quantum groups

AbstractThe Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been

ELLIPTIC ALGEBRA AQ,P(SL2) IN THE SCALING LIMIT

The scaling limit Ah̄,η(ŝl2) of the elliptic algebra Aq,p(ŝl2) is investigated. The limiting algebra is defined in terms of a continuous family of generators being Fourier harmonics of Gauss

ELLIPTIC QUANTUM GROUPS E τ,η ( sl 2 ) AND QUASI-HOPF ALGEBRAS

. We construct an algebra morphism from the elliptic quantum group E τ,η ( sl 2 ) to a certain elliptic version of the “quantum loop groups in higher genus” studied by V. Rubtsov and the first author.

An Elliptic Algebra and the Fusion RSOS Model

Abstract:We introduce an elliptic algebra with and present its free boson representation at generic level k. We show that this algebra governs a structure of the space of states in the k-fusion RSOS

The Elliptic Algebra U_{q,p}(sl_N^) and the Deformation of W_N Algebra

After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra U_{q,p}(sl_N^), we investigate a fusion of the