University of Illinois Urbana-Champaign

Wreath Macdonald polynomials as eigenstates

Wen, Joshua Jeishing

Content Files
WEN-DISSERTATION-2020.pdf

Permalink

https://hdl.handle.net/2142/108489

Description

Title
Wreath Macdonald polynomials as eigenstates
Author(s)
Wen, Joshua Jeishing
Issue Date
2020-07-16
Director of Research (if dissertation) or Advisor (if thesis)
Dodd, Christopher
Doctoral Committee Chair(s)
Kedem, Rinat
Committee Member(s)
  • di Francesco, Philippe
  • Katz, Sheldon
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2020-10-07T20:59:51Z
Keyword(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.
Graduation Semester
2020-08
Type of Resource
Thesis
Permalink
http://hdl.handle.net/2142/108489
Copyright and License Information
Copyright 2020 Joshua Wen

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