This returns the ring of coefficients of the quantized enveloping algebra U.
This returns the root datum corresponding to the quantized enveloping algebra U.
Given a quantized universal enveloping algebra U with root datum R returns a sequence consisting of the integers between 1 and the number of positive roots of R. If the k-th element of this sequence is m, then the generator Fk of U is of weight -βm, where βm is the m-th positive root of R (as returned by PositiveRoots(R)). (For the definition of weight of an element of U see Section PBW-type Bases.) Furthermore, the generator Ek is of weight βm.
> R:= RootDatum("D4"); > U:= QuantizedUEA(R); > CoefficientRing(U); Univariate rational function field over Rational Field Variables: q > RootDatum(U); Adjoint root datum of type D4 > PositiveRootsPerm(U); [ 1, 5, 2, 8, 6, 3, 12, 11, 9, 10, 7, 4 ]So for instance this means that F6 is of weight -β3.