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en Copyright 2020 Joshua Wen Macdonald polynomials quantum toroidal algebras Wreath Macdonald polynomials as eigenstates text Thesis Dodd, Christopher Kedem, Rinat di Francesco, Philippe Katz, Sheldon Wen, Joshua Jeishing 2020-10-07T20:59:51Z 2020-10-07T20:59:51Z 2020-07-16 2020-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms The student, Joshua Wen, accepted the attached license on 2020-07-14 at 13:25. The student, Joshua Wen, submitted this Dissertation for approval on 2020-07-14 at 13:29. This Dissertation was approved for publication on 2020-07-16 at 15:33. DSpace SAF Submission Ingestion Package generated from Vireo submission #15608 on 2020-10-02 at 15:13:23 Made available in DSpace on 2020-10-07T20:59:51Z (GMT). No. of bitstreams: 2 WEN-DISSERTATION-2020.pdf: 588045 bytes, checksum: 573aae6094903cd7c38ef3f7fe2ee709 (MD5) LICENSE.txt: 4207 bytes, checksum: 0435b2885ffb9acd03888ac66039f5d8 (MD5) Previous issue date: 2020-07-16 application/pdf http://hdl.handle.net/2142/108489 Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.