  The characters of irreducible finite dimensional representations of compact
simple Lie group G are invariant with respect to the action of the Weyl group
W(G) of G. The defining property of the new character-like functions ("hybrid
characters") is the fact that W(G) acts differently on the character term
corresponding to the long roots than on those corresponding to the short roots.
Therefore the hybrid characters are defined for the simple Lie groups with two
different lengths of their roots. Dominant weight multiplicities for the hybrid
characters are determined. The formulas for "hybrid dimensions" are also found
for all cases as the zero degree term in power expansion of the "hybrid
characters".
