The twisted Cherednik spectrum is a q,t-deformation of the polynomial eigenfunctions built from symmetric ground states and weak-composition excitations at q=1.
The affine Yangian of $\mathfrak{gl}_1$ revisited
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The affine Yangian of $\mathfrak{gl}_1$ has recently appeared simultaneously in the work of Maulik-Okounkov and Schiffmann-Vasserot in connection with the Alday-Gaiotto-Tachikawa conjecture. While the former presentation is purely geometric, the latter algebraic presentation is quite involved. In this article, we provide a simple loop realization of this algebra which can be viewed as an "additivization" of the quantum toroidal algebra of $\mathfrak{gl}_1$ in the same way as the Yangian $Y_h(\mathfrak{g})$ is an "additivization" of the quantum loop algebra $U_q(L\mathfrak{g})$ for a simple Lie algebra $\mathfrak{g}$. We also explain the similarity between the representation theories of the affine Yangian and the quantum toroidal algebras of $\mathfrak{gl}_1$ by generalizing the milestone result of Gautam and Toledano Laredo to the current settings.
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UNVERDICTED 3representative citing papers
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
Non-commutative creation operators B̂_m are built for symmetric polynomials in matrix and Fock representations of W_{1+∞} and affine Yangian algebras.
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Twisted Cherednik spectrum as a $q,t$-deformation
The twisted Cherednik spectrum is a q,t-deformation of the polynomial eigenfunctions built from symmetric ground states and weak-composition excitations at q=1.
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Quiver Yangians as Coulomb branch algebras
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
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Non-commutative creation operators for symmetric polynomials
Non-commutative creation operators B̂_m are built for symmetric polynomials in matrix and Fock representations of W_{1+∞} and affine Yangian algebras.