The Delta Conjecture at 𝑞=1

Romero, Marino

doi:10.1090/tran/7140

The Delta Conjecture at $q = 1$
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Trans. Amer. Math. Soc. 369 (2017), 7509-7530 Request permission

Abstract:

We use a weight-preserving, sign-reversing involution to find a combinatorial expansion of $\Delta _{e_k} e_n$ at $q=1$ in terms of the elementary symmetric function basis. We then use a weight-preserving bijection to prove the Delta Conjecture of Haglund, Remmel, and Wilson at $q=1$. The method of proof provides a variety of structures which can compute the inner product of $\Delta _{e_k} e_n|_{q=1}$ with any symmetric function.

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