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. 
Jos\'e Fern\'andez Nu\~nez, Wifredo Garc\'ia Fuertes and Askold M.   Perelomov
math-ph math.MP