What is a formula for the "group-like Drinfeld element"? Any quantized universal enveloping algebra (in fact, any toplogically quasi-triangular Hopf algebra) has an (in its completion) an element u called the Drinfeld element which gives an isomorphism from a representation to its double dual.
However, most people prefer to use a different pivotal structure on the category of representations of the quantized universal enveloping algebra, where u is replaced by g=v-1u.  Several obvious references don't seem to have a formula for this element, even though my dim recollection is that it is very simple.  Is there anywhere where this is written down properly?
 A: Up to sign conventions it's just K_\rho, where \rho is the Weyl vector (half the sum of the positive roots).  It's easy to check that this does satisfy the basic properties of g, namely that it is grouplike and that conjugation by it acts by S^2.  Thus it gives a pivotal structure.  (You still need to check that it actually is the g that comes from the usual ribbon element, which is a bit more delicate.)
A: It looks like your question was already answered, but I highly recommend the book by Klymik and Schüdgen for this sort of question.  In particular, they spell out the formula for a ribbon element in a QUE's quite explicitly as I recall.  Both an advantage and a drawback of that book are that they do everything very explicitly with formulas.
I could be wrong (don't have a text with me) but I thought that the formula was a slight modification of what Noah wrote: namely one takes as a first guess u=\mu(R_21 R_12), i.e. you take the two components of the squared R-matrix and multiply them.  This is almost a ribbon element; it satifies a coproduct relation similar to the ribbon element, and more precisely, uS(u) is the square of the actual ribbon element.  Thus, u has to be corrected by the factor Noah mentioned, e^{-h\rho}.  In the end, I believe the ribbon element is e^{-h rho}u.
A: Could this be related to Drinfeld associator?
