Equivariant Chern character operators and Okounkov's conjecture

2025/05/20 by Alhwaimel, Mazen M., Qin, Zhenbo · 1 citation
#17B69 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 14C05 #Representation Theory (math.RT) #Secondary 11B65

paper · doi:10.48550/arxiv.2505.14626

Abstract

In this paper, we study the Chern character operators on the equivariant cohomology of the Hilbert schemes of points in the complex affine plane C² with the action of the torus (C^*)², and partially verify Okounkov's Conjecture [Oko, Conjecture 2] in this setting. Our main idea is to apply the connection between the equivariant cohomology of these Hilbert schemes and the ring of symmetric functions, via the deformed vertex operators of Cheng and Wang [CW], (the integral form of) the Jack symmetric functions and the transformed Macdonald symmetric functions of Garsia and Haiman [GH, Hai].

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Cited by

• Multiple q-zeta values and traces

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• Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane
• Equivariant Cohomological Chern Characters
• On Okounkov's conjecture connecting Hilbert schemes of points and multiple q-zeta values
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• Equivariant relative Thom forms and Chern characters