English

Elliptic Quantum Groups U_{q,p}(gl_N) and E_{q,p}(gl_N)

Quantum Algebra 2016-10-04 v2 High Energy Physics - Theory Mathematical Physics Algebraic Geometry math.MP Representation Theory

Abstract

We reformurate a central extension of Felder's elliptic quantum group in the FRST formulation as a topological algebra E_{q,p}(gl_N) over the ring of formal power series in p. We then discuss the isomorphism between E_{q,p}(gl_N) and the elliptic algebra U_{q,p}(gl_N) of the Drinfeld realization. An evaluation H-algebra homomorphism from U_{q,p}(gl_N) to a dynamical extension of the quantum affine algebra U_q(gl_N) resolves the problem into the one discussed by Ding and Frenkel in the trigonometric case. We also provide some useful formulas for the elliptic quantum determinants.

Keywords

Cite

@article{arxiv.1603.04129,
  title  = {Elliptic Quantum Groups U_{q,p}(gl_N) and E_{q,p}(gl_N)},
  author = {Hitoshi Konno},
  journal= {arXiv preprint arXiv:1603.04129},
  year   = {2016}
}

Comments

60 pages; v2: typos corrected. To appear in Advanced Studies in Pure Mathematics

R2 v1 2026-06-22T13:09:56.555Z