On the q-commutations in Uq(n) at roots of one

[摘要] Let epsilon be a root of one and g a semisimple Lie algebra with triangular decomposition g = n + h + n(-). Let U-s(+) (resp. U-epsilon(res+)) be the nonrestricted (resp. restricted) quantum enveloping algebra of n. We prove that Fract U-epsilon(+) is a quantum Weyl field. We then give a description of the E-center of U-epsilon(+). Let U-epsilon(fin+) be the finite part of U-epsilon(res+). Via the Drinfeld correspondence, the U-epsilon(fin+)-covariant space of a Weyl module is epsilon-central. In case g = sl(n), this enables us to describe this space in terms of semistandard Young tableaux. (C) 1998 Academic Press.

[发布日期] 1998-12-15