Report
A geometric interpretation of the Delta Conjecture
| العنوان: | A geometric interpretation of the Delta Conjecture |
|---|---|
| المؤلفون: | Gillespie, Maria, Gorsky, Eugene, Griffin, Sean T. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Algebraic Geometry |
| الوصف: | We introduce a variety $Y_{n,k}$, which we call the \textit{affine $\Delta$-Springer fiber}, generalizing the affine Springer fiber studied by Hikita, whose Borel-Moore homology has an $S_n$ action and a bigrading that corresponds to the Delta Conjecture symmetric function $\mathrm{rev}_q\,\omega \Delta'_{e_{k-1}}e_n$ under the Frobenius character map. We similarly provide a geometric interpretation for the Rational Shuffle Theorem in the integer slope case $(km,k)$. The variety $Y_{n,k}$ has a map to the affine Grassmannian whose fibers are the $\Delta$-Springer fibers introduced by Levinson, Woo, and the third author. Part of our proof of our geometric realization relies on our previous work on a Schur skewing operator formula relating the Rational Shuffle Theorem to the Delta Conjecture. Comment: 39 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2501.00197 |
| رقم الانضمام: | edsarx.2501.00197 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |