Monday, May 7, 2012

1205.0904 (Francis W. Lemire et al.)

Decompositions of hybrid characters in terms of orbit functions    [PDF]

Francis W. Lemire, Jiri Patera, Marzena Szajewska
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 function ('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 zero degree term in power expansion of the 'hybrid characters'.
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