ar X iv : 1 71 0 . 07 07 8 v 1 [ m at h . C O ] 1 9 O ct 2 01 7 A PROOF OF THE DELTA CONJECTURE WHEN q = 0
نویسنده
چکیده
In [The Delta Conjecture, Trans. Amer. Math. Soc., to appear] Haglund, Remmel, Wilson introduce a conjecture which gives a combinatorial prediction for the result of applying a certain operator to an elementary symmetric function. This operator, defined in terms of its action on the modified Macdonald basis, has played a role in work of Garsia and Haiman on diagonal harmonics, the Hilbert scheme, and Macdonald polynomials [A. M. Garsia and M. Haiman. A remarkable q, t-Catalan sequence and q-Lagrange inversion, J. Algebraic Combin. 5 (1996), 191–244], [M. Haiman, Vanishing theorems and character formulas for the Hilbert scheme of points in the plane, Invent. Math. 149 (2002), 371-407]. The Delta Conjecture involves two parameters q, t; in this article we give the first proof that the Delta Conjecture is true when q = 0 or t = 0.
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