Computes multiplicities of core Lagrangians in Hilbert schemes on elliptic surfaces and proposes mirror duality of very stable upward flows to modified Procesi bundles, supported by numerical checks and conjectures for wobbly cases.
Jack polynomials and Hilbert schemes of points on surfaces
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The Jack symmetric polynomials $P_\lambda^{(\alpha)}$ form a class of symmetric polynomials which are indexed by a partition $\lambda$ and depend rationally on a parameter $\alpha$. They reduced to the Schur polynomials when $\alpha=1$, and to other classical families of symmetric polynomials for several specific parameters. It is well-known that Schur polynomials can be realized as certain elements of homology groups of Grassmann manifolds. The purpose of this paper is to give a similar geometric realization for Jack polynomials. However, spaces which we use are totally different. Our spaces are Hilbert schemes of points on a surface X which is the total space of a line bundle L over the projective line. The parameter $\alpha$ in Jack polynomials relates to our surface X by $\alpha = -<C,C>$, where C is the zero section, and <C,C> is the self-intersection number of C.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proposes solvable interpolations between small and large equivariant parameter regimes in Gromov-Witten theory on P1 as analogue for AdS3/CFT2 transitions, plus string theory embedding of P1 x C2 correspondence and Jack polynomial analysis of scaling limit.
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Equivariant multiplicities and mirror symmetry for Hilbert schemes
Computes multiplicities of core Lagrangians in Hilbert schemes on elliptic surfaces and proposes mirror duality of very stable upward flows to modified Procesi bundles, supported by numerical checks and conjectures for wobbly cases.
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Equivariant Interpolations in Topological Holography
Proposes solvable interpolations between small and large equivariant parameter regimes in Gromov-Witten theory on P1 as analogue for AdS3/CFT2 transitions, plus string theory embedding of P1 x C2 correspondence and Jack polynomial analysis of scaling limit.