Browsing by Subject "Quantum toroidal"

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    Braid actions on quantum toroidal superalgebras
    (Elsevier, 2021-11) Bezerra, Luan; Mukhin, Evgeny; Mathematical Sciences, School of Science
    We prove that the quantum toroidal algebras Es associated with different root systems s of glm|n type are isomorphic. We also show the existence of Miki automorphism of Es, which exchanges the vertical and horizontal subalgebras. To obtain these results, we establish an action of the toroidal braid group on the direct sum ⊕sEs of all such algebras.
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    Quantum Toroidal Superalgebras
    (2020-05) Pereira Bezerra, Luan; Mukhin, Evgeny; Ramras, Daniel; Roeder, Roland; Tarasov, Vitaly
    We introduce the quantum toroidal superalgebra E(m|n) associated with the Lie superalgebra gl(m|n) and initiate its study. For each choice of parity "s" of gl(m|n), a corresponding quantum toroidal superalgebra E(s) is defined. To show that all such superalgebras are isomorphic, an action of the toroidal braid group is constructed. The superalgebra E(s) contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uq sl̂(m|n) with parity "s", called vertical and horizontal subalgebras. We show the existence of Miki automorphism of E(s), which exchanges the vertical and horizontal subalgebras. If m and n are different and "s" is standard, we give a construction of level 1 E(m|n)-modules through vertex operators. We also construct an evaluation map from E(m|n)(q1,q2,q3) to the quantum affine algebra Uq gl̂(m|n) at level c=q3^(m-n)/2.