Abstract
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’.
Highlights
The character of an irreducible finite dimensional representation of a compact simple Lie group contains, in principle, all the information one may want to know about the representation
The hybrid characters of this paper lead to new classes of special functions that are orthogonal on lattices of all dimensions and symmetry types
For that to be used, one needs the dominant weight multiplicities of the hybrid characters for every representation that comes into considerations
Summary
The character of an irreducible finite dimensional representation of a compact simple Lie group contains, in principle, all the information one may want to know about the representation. In this paper the problem of multiplicities of weights is solved for the recently discovered character-like functions (denoted by χλL(g) and χλS(g)), called hybrid characters [24, 31], for any simple Lie group with roots of two different lengths The present paper solves the problem of determining the coefficients pμλ (g) and qμλ(g) arising in χλL(g) and χλS(g) respectively, when the hybrid characters are written as linear combinations of the C-functions. The new classes of character-like functions are formed by defining two new homomorphisms from the Weyl group W (g) of the simple Lie algebra g to {±1} which generalize the usual sign function.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
