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1. The affine Springer fiber – sheaf correspondence

   https://doi.org/10.1016/j.aim.2025.110143  

   Gorsky, Eugene; Kivinen, Oscar; Oblomkov, Alexei (March 2025, Advances in Mathematics)
2. Springer correspondence for the split symmetric pair in type

   https://doi.org/10.1112/S0010437X18007443  

   Chen, Tsao-Hsien; Vilonen, Kari; Xue, Ting (November 2018, Compositio Mathematica)

   In this paper we establish Springer correspondence for the symmetric pair $$(\text{SL}(N),\text{SO}(N))$$ using Fourier transform, parabolic induction functor, and a nearby cycle sheaf construction. As an application of our results we see that the cohomology of Hessenberg varieties can be expressed in terms of irreducible representations of Hecke algebras of symmetric groups at $q=-1$ . Conversely, we see that the irreducible representations of Hecke algebras of symmetric groups at $q=-1$ arise in geometry. 

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3. Particularity 2023. Particularity. In. New York: Springer. To appear.

   Spector, L.; Ding, L; Boldi, R. (January 2023, Genetic Programming Theory and Practice XX)

   We describe a design principle for adaptive systems under which adaptation is driven by particular challenges that the environment poses, as opposed to average or otherwise aggregated measures of performance over many challenges. We trace the development of this "particularity" approach from the use of lexicase selection in genetic programming to "particularist" approaches to other forms of machine learning and to the design of adaptive systems more generally. 

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4. A cocharge formula for the ∆-Springer modules

   Gillespie, Maria; Griffin, Sean T (April 2023, Séminaire Lotharingien de Combinatoire)

   We conjecture a simple combinatorial formula for the Schur expansion of the Frobenius series of the Sn-modules Rn,λ,s, which appear as the cohomology rings of the “∆-Springer” varieties. These modules interpolate between the Garsia-Procesi modules Rµ (which are the type A Springer fiber cohomology rings) and the rings Rn,k defined by Haglund, Rhoades, and Shimozono in the context of the Delta Conjecture. Our formula directly generalizes the known cocharge formula for Garsia-Procesi modules and gives a new cocharge formula for the Delta Conjecture at t = 0, by introducing battery-powered tableaux that “store” extra charge in their battery. Our conjecture has been verified by computer for all n ≤ 10 and s ≤ ℓ(λ)+2, as well as for n ≤ 8 and s ≤ ℓ(λ)+7. We prove it holds for several infinite families of n,λ,s. 

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5. A new approach to the generalized Springer correspondence

   https://doi.org/10.1090/tran/8890  

   Graham, William; Precup, Martha; Russell, Amber (June 2023, Transactions of the American Mathematical Society)

   The Springer resolution of the nilpotent cone is used to give a geometric construction of the irreducible representations of Weyl groups. Borho and MacPherson obtain the Springer correspondence by applying the decomposition theorem to the Springer resolution, establishing an injective map from the set of irreducible Weyl group representations to simple equivariant perverse sheaves on the nilpotent cone. In this manuscript, we consider a generalization of the Springer resolution using a variety defined by the first author. Our main result shows that in the type A case, applying the decomposition theorem to this map yields all simple perverse sheaves on the nilpotent cone with multiplicity as predicted by Lusztig’s generalized Springer correspondence. 

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