PIRSA:19010067 Scientific Series Mathematical physics

DOI10.48660/19010067

Series: Mathematical Physics

Konno, H. (2019). REPRESENTATIONS OF THE ELLIPTIC QUANTUM GROUP AND RELATED GEOMETRY. Perimeter Institute. https://pirsa.org/19010067

Konno, Hitoshi. REPRESENTATIONS OF THE ELLIPTIC QUANTUM GROUP AND RELATED GEOMETRY. Perimeter Institute, Jan. 14, 2019, https://pirsa.org/19010067 

@misc{ pirsa_PIRSA:19010067,
  doi = {10.48660/19010067},
  url = {https://pirsa.org/19010067},
  author = {Konno, Hitoshi},
  keywords = {Mathematical physics},
  language = {en},
  title = {REPRESENTATIONS OF THE ELLIPTIC QUANTUM GROUP AND RELATED GEOMETRY},
  publisher = {Perimeter Institute},
  year = {2019},
  month = {jan},
  note = {PIRSA:19010067 see, \url{https://pirsa.org}}
}

Abstract

 

The elliptic quantum (toroidal) group U_{q,p}(g) is an elliptic and dynamical analogue of the Drinfeld realization 
of the affine quantum (toroidal) group U_q(g). I will discuss an interesting connection of its representations with 
a geometry such as an identification of the elliptic weight functions derived by using  the vertex operators with 
the elliptic stable envelopes in [Aganagic-  Okounkov ’16] and correspondence between the Gelfand-Tsetlin bases 
of a finite dimensional representation of U_{q,p} with the fixed point classes in the equivariant elliptic cohomology.

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