A note on Franel numbers and $SU(3)$
We study weight multiplicities in tensor powers of the adjoint representation of $SU(3)$ and relate them to Franel numbers.
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arXiv subjects
Askold M. Perelomov
Publications and source records attributed to Askold M. Perelomov.
Some results on generating functions for characters and weight multiplicities of the Lie algebra $A_3$
A method based on the quantum Calogero-Sutherland model is used to obtain generating functions for characters and multiplicities of $A_3$. Some comments on other rank three algebras are offered.
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Generating functions and multiplicity formulas: the case of rank two simple Lie algebras
A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from $H$ explicit multiplicity formulas for particular weights is explained and the results corresponding to rank two simple Lie algebras shown.
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On the generating function of weight multiplicities for the representations of the Lie algebra $C_2$
We use the generating function of the characters of $C_2$ to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function we derive some recurrence relations among the multiplicities and a simple graphical recipe to compute them.
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