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
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.
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