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- W4385436246 abstract "We prove that $omega Delta'_{e_{k}}e_n|_{t=0}$, the symmetric function in the Delta Conjecture at $t=0$, is a skewing operator applied to a Hall-Littlewood polynomial, and generalize this formula to the Frobenius series of all $Delta$-Springer modules. We use this to give an explicit Schur expansion in terms of the Lascoux-Schutzenberger cocharge statistic on a new combinatorial object that we call a textit{battery-powered tableau}. Our proof is geometric, and shows that the $Delta$-Springer varieties of Levinson, Woo, and the second author are generalized Springer fibers coming from the partial resolutions of the nilpotent cone due to Borho and MacPherson. We also give alternative combinatorial proofs of our Schur expansion for several special cases, and give conjectural skewing formulas for the $t$ and $t^2$ coefficients of $omega Delta'_{e_{k}}e_n$." @default.
- W4385436246 created "2023-08-01" @default.
- W4385436246 creator A5051456056 @default.
- W4385436246 creator A5060560113 @default.
- W4385436246 date "2023-07-05" @default.
- W4385436246 modified "2023-10-16" @default.
- W4385436246 title "Cocharge and skewing formulas for $Delta$-Springer modules and the Delta Conjecture" @default.
- W4385436246 doi "https://doi.org/10.48550/arxiv.2307.02645" @default.
- W4385436246 hasPublicationYear "2023" @default.
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