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