Dominant weight multiplicities in hybrid characters of \(B_n\), \(C_n\), \(F_4\), \(G_2\). (English) Zbl 1329.81204
Summary: 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’.
MSC:
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
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