Small Elliptic Quantum Group $e_{tau,γ}(sl_N)$

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dc.creatorTarasov, V.
dc.creatorVarchenko, A.
dc.date2000-11-20
dc.date2001-05-14
dc.date.accessioned2026-07-07T04:38:42Z
dc.date.available2026-07-07T04:38:42Z
dc.descriptionThe small elliptic quantum group $e_{τ,γ}(sl_N)$, introduced in the paper, is an elliptic dynamical analogue of the universal enveloping algebra $U(sl_n)$. We define highest weight modules, Verma modules and contragradient modules over $e_{τ,γ}(sl_N)$, the dynamical Shapovalov form for $e_{τ,γ}(sl_N)$ and the contravariant form for highest weight $e_{τ,γ}(sl_N)$-modules. We show that any finite-dimensional $sl_N$-module and any Verma module over $sl_N$ can be lifted to the corresponding $e_{τ,γ}(sl_N)$-module on the same vector space. For the elliptic quantum group $E_{τ,γ}(sl_N)$ we construct the evaluation morphism $E_{τ,γ}(sl_N)\to e_{τ,γ}(sl_N)$, thus making any $e_{τ,γ}(sl_N)$-module into an evaluation $E_{τ,γ}(sl_N)$-module.
dc.description34 pages, amstex.tex (ver. 2.1), misprints are corrected
dc.identifierhttps://arxiv.org/abs/math/0011145
dc.identifierhttp://arxiv.org/abs/math/0011145
dc.identifierMoscow Math. J. 1 (2001) no.2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60384
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.titleSmall Elliptic Quantum Group $e_{tau,γ}(sl_N)$
dc.typetext

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