On theq-Commutations inUq(n) at Roots of One

AbstractLet ε be a root of one and g a semisimple Lie algebra with triangular decomposition g=n+h+n−. LetU+ε(resp.Ures+ε) be the nonrestricted (resp. restricted) quantum enveloping algebra of n. We prove that FractU+εis a quantum Weyl field. We then give a description of the ε-center ofU+ε. LetUfin+εbe the finite part ofUres+ε. Via the Drinfeld correspondence, theUfin+ε-covariant space of a Weyl module is ε-central. In case g=sln, this enables us to describe this space in terms of semistandard Young tableaux