arXiv:2610.31794v1 Announce Type: new Abstract: In this work, we study the Hamiltonian reduction, used in constructing finite rectangular $W$-algebras, of the big-cell differential realization of $\mathfrak{gl}_{np}$. We establish an intrinsic factorization of the reduced differential realization, identifying its Yangian action with the coproduct action on a tensor product of $n$ evaluation differential realizations of $\mathfrak{gl}_p$. Corner quasideterminants provide the essential noncommutative mechanism through which Hamiltonian reduction transforms the higher-rank differential realization into a factorized lower-rank Yangian action.
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