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Showing 1 to 4 of 4 for “"Quantum toroidal"”.
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Quantum Toroidal Superalgebras
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 …
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Miki Images of Quantum Toroidal Algebra Generators in the Shuffle Algebra
… calculations of the images of generators of the quantum toroidal algebra. We will be working in the small shuffle algebra, which is isomorphic to the positive part of the quantum toroidal algebra. There, we will be computing commutators, which are equal to images under the Miki automorphism, …
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Wreath Macdonald polynomials as eigenstates
… as elements in the vertex representation of the quantum toroidal algebra $U_{\qqq,\ddd}(\ddot{\mathfrak{sl}}_\ell)$, diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods.
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The affine Yangian of gl₁, and the infinitesimal Cherednik algebras
… considered in the work of Maulik-Okounkov on the quantum cohomology theory, see [MO]. We present a purely algebraic realization of these algebras by generators and relations. We discuss some families of their representations. A similarity with the representation theory of the quantum toroidal …