Dominant weight multiplicities in hybrid characters of Bn, Cn, F4, G2

Francis W. Lemire, Jiri Patera, Marzena Szajewska

Published 2012-05-04, updated 2014-09-01Version 3

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".