A Pieri formula for the characters of complex simple Lie algebras. (English) Zbl 07815443
Summary: A Pieri formula is presented for the characters of complex simple Lie algebras of arbitrary Dynkin type, providing the decomposition of the tensor product of a general irreducible representation with one taken from a particular subclass of very small representations. The class of very small irreducible representations under consideration exceeds the minuscule and quasi-minuscule representations and includes in particular all fundamental representations in the case of a classical Lie algebra.
MSC:
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 05E05 | Symmetric functions and generalizations |
| 05E10 | Combinatorial aspects of representation theory |
| 17B20 | Simple, semisimple, reductive (super)algebras |
| 22E46 | Semisimple Lie groups and their representations |
| 33C52 | Orthogonal polynomials and functions associated with root systems |
Keywords:
simple Lie algebras/groups; irreducible representations; character ring; Pieri rule; symmetric functionsReferences:
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