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math.RT2025

Elliptic Quantum Toroidal Algebra and Elliptic Stable Envelopes for the Quiver Varieties

Hitoshi Konno, Andrey Smirnov

We propose a new construction of vertex operators of the elliptic quantum toroidal algebra by combining representations of the algebra and fo…

math.RT2025

Elliptic Quantum Toroidal Algebra U_{t_1,t_2,p}(gl_{1,tor}), Vertex Operators and L-operators

Hitoshi Konno, Andrey Smirnov

We propose new vertex operators, both the type I and the type II dual, of the elliptic quantum toroidal algebra U_{t_1,t_2,p}(gl_{1,tor}) by combining representations of U_{t_1,t_2…

math.RT2024

Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations

Hitoshi Konno, Kazuyuki Oshima

We introduce a new elliptic quantum toroidal algebra U_{q,κ,p}(g_tor) associated with an arbitrary toroidal algebra g_tor. We show that U_{q,κ,p}(g_tor) contains two elliptic qua…