Cyclotomic expansions for glN link invariants via interpolation Macdonald polynomials

• Anna Beliakova ^[1] ; Eugene Gorsky ^[2]
  1. [1] University of Zurich

     University of Zurich

     Zürich, Suiza

     
  2. [2] University of California System

     University of California System

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024
• Idioma: inglés
• DOI: 10.1007/s00029-024-00990-y
• Enlaces
  • Texto completo
• Resumen

  • In this paper we construct a new basis for the cyclotomic completion of the center of the quantum glN in terms of the interpolation Macdonald polynomials. Then we use a result of Okounkov to provide a dual basis with respect to the quantum Killing form (or Hopf pairing). The main applications are: 1) cyclotomic expansions for the glN Reshetikhin–Turaev link invariants and the universal glN knot invariant; 2) an explicit construction of the unified glN invariants for integral homology 3-spheres using universal Kirby colors. These results generalize those of Habiro for sl2. In addition, we give a simple proof of the fact that the universal glN invariant of any evenly framed link and the universal slN invariant of any 0-framed algebraically split link are Γ-invariant, where Γ=Y/2Y with the root lattice Y.

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