This analysis reveals commutative subalgebras and eigenvalue properties in Schur polynomial algebras, highlighting their relation to Yangians.
We consider algebras acting on Schur and Q-Schur polynomials, corresponding to Kadomtsev-Petviashvili (KP) and BKP hierarchies. We present them in the spirit of affine Yangians, paying special attention to commutative subalgebras, box additivity property of eigenvalues and single hook expansion of operators.
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Nikita Tselousov (2025) studied this question.
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