On Combinatorics of Quiver Component Formulas
نویسنده
چکیده
Buch and Fulton [7] conjectured the nonnegativity of the quiver coefficients appearing in their formula for a quiver variety. Knutson, Miller and Shimozono [21] proved this conjecture as an immediate consequence of their “component formula”. We present an alternative proof of the component formula by substituting combinatorics for Gröbner degeneration [21, 20]. We relate the component formula to the work of Buch, Kresch, Tamvakis and the author [8] where a “splitting” formula for Schubert polynomials in terms of quiver coefficients was obtained. We prove analogues of this latter result for the type BCD-Schubert polynomials of Billey and Haiman [4].
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