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 F
6 is of weight -β
3.
V2.28, 13 July 2023