The universal character ring for the general linear group is well understood but I want to ask about the universal character ring for the symplectic and orthogonal groups. For the general linear group, it is the projective limit of the system of the graded algebra consisting of symmetric polynomials in n variables. Please suggests any source where I can read this for the other group in every detail. I discovered the term 'universal character ring' when I was reading the following paper by Koike, Kazuhiko; Terada, Itaru, Young-diagrammatic methods for the representation theory of the classical groups of type (B_ n), (C_ n), (D_ n), J. Algebra 107, 466-511 (1987). ZBL0622.20033.
1 Answer
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I suggest the following:
M. J. Newell, Modification Rules for the Orthogonal and Symplectic Groups. Proc. Roy. Irish Acad. 54, 153 (1951),
R. C. King, Modification Rules and Products of Irreducible Representations of the Unitary, Orthogonal, and Symplectic Groups. J. Math. Phys. 12, 1588 (1971).
G. R. E. Black, R. C. King and B. G. Wybourne, Kronecker products for compact semisimple Lie groups. J. Phys. A: Math. Gen. 16, 1555 (1983).