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.
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