Springer fibers and the Delta Conjecture at t = 0
We introduce a family of varieties Yn,λ,s, which we call the Δ-Springer varieties, that generalize the type A Springer fibers. We give an explicit presentation of the cohomology ring H⁎(Yn,λ,s) and show that there is a symmetric group action on this ring generalizing the Springer action on the cohom...
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| Published in: | Advances in mathematics (New York. 1965) 2024-03, Vol.439, p.109491, Article 109491 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | We introduce a family of varieties Yn,λ,s, which we call the Δ-Springer varieties, that generalize the type A Springer fibers. We give an explicit presentation of the cohomology ring H⁎(Yn,λ,s) and show that there is a symmetric group action on this ring generalizing the Springer action on the cohomology of a Springer fiber. In particular, the top cohomology groups are induction products of Specht modules with trivial modules. The λ=(1k) case of this construction gives a compact geometric realization for the expression in the Delta Conjecture at t=0. Finally, we generalize results of De Concini and Procesi on the scheme of diagonal nilpotent matrices by constructing an ind-variety Yn,λ whose cohomology ring is isomorphic to the coordinate ring of the scheme-theoretic intersection of an Eisenbud–Saltman rank variety and diagonal matrices. |
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| ISSN: | 0001-8708 1090-2082 |