We show that the combinatorial definitions of King and Sundaram of the symmetric polynomials of types B and C are indeed symmetric, in the sense that they are invariant by the action of the Weyl groups. Our proof is combinatorial and inspired by Bender and Knuth's classic involutions for type A.
Equivalence Classes in the Weyl groups of type $B_n$
Symmetric polynomials associated with numerical semigroups
The Hecke algebra and structure constants of the ring of symmetric polynomials
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