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Counterexamples to the Reiner-Shimozono conjecture and the failure of Schubert filtrations
We disprove the Reiner--Shimozono conjecture that products of key polynomials have nonnegative expansions in Demazure atoms. By relaxing the defining relations of Demazure modules, we obtain an exact coefficient-extraction formula that yields an explicit infinite family of counterexamples, including
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