Given a monomial m in U^ - for some quantized
enveloping algebra U, i.e., m must be a monomial in the first
n generators of U, where n is the number of positive roots
of the corresponding root datum, returns another monomial
in the negative part of U that is obtained by applying the i-th
Kashiwara operator tilde(F)i to m (see Section The Canonical Basis).
Here i must lie between 1 and the rank of the root datum.
Given a monomial m in U^ - for some quantized
enveloping algebra U, i.e., m must be a monomial in the first
n generators of U, where n is the number of positive roots
of the corresponding root datum, return
tilde(E)i(m) (see Section The Canonical Basis)
if the i-th Kashiwara operator
tilde(E)i is applicable to m.
Otherwise the zero
element of U is returned. Here i must lie between 1 and the
rank of the root datum.
> R:= RootDatum("F4");
> U:= QuantizedUEA(R);
> m:= U.1*U.5*U.10*U.18*U.24;
> m;
F_1*F_5*F_10*F_18*F_24
> Falpha(m, 3);
F_1*F_6*F_7*F_10*F_18*F_24
> Ealpha(m, 4);
F_1*F_4*F_5*F_7*F_9*F_18*F_24
> Ealpha(m, 2);
0
V2.28, 13 July 2023