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Title:Wreath Macdonald polynomials as eigenstates
Author(s):Wen, Joshua Jeishing
Director of Research:Dodd, Christopher
Doctoral Committee Chair(s):Kedem, Rinat
Doctoral Committee Member(s):di Francesco, Philippe; Katz, Sheldon
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Macdonald polynomials
quantum toroidal algebras
Abstract:We show that the wreath Macdonald polynomials for $\ZZ/\ell\ZZ\wr\Sigma_n$, when naturally viewed 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.
Issue Date:2020-07-16
Type:Thesis
URI:http://hdl.handle.net/2142/108489
Rights Information:Copyright 2020 Joshua Wen
Date Available in IDEALS:2020-10-07
Date Deposited:2020-08


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