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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2602.08366 |
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| _version_ | 1866917259636637696 |
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| author | Zhukov, Evgeny |
| author_facet | Zhukov, Evgeny |
| contents | We study the manifold $Q_{Γ, λ}$ of isospectral real skew-symmetric matrices with a prescribed sparsity pattern determined by a graph $Γ$. The compact torus $T^n$ acts naturally on $Q_{Γ,λ}$ by conjugation, and this action can be studied using GKM theory. We prove two results about this manifold and its GKM graph. The first theorem describes how the GKM graph of $Q_{Γ, λ}$ is obtained from the GKM graph of the corresponding manifold $M_{Γ, λ}$ of isospectral Hermitian matrices. The second theorem gives a criterion for equivariant formality of $Q_{Γ, λ}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08366 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | GKM Theory for Manifolds of Isospectral Matrices in Lie Type D Zhukov, Evgeny Algebraic Topology Combinatorics 15B57, 57R91, 57S12, 14M15, 55N91 (Primary) 57R19, 15A18, 57S25, 05C25, 05C76, 15B30, 17B99 (Secondary) We study the manifold $Q_{Γ, λ}$ of isospectral real skew-symmetric matrices with a prescribed sparsity pattern determined by a graph $Γ$. The compact torus $T^n$ acts naturally on $Q_{Γ,λ}$ by conjugation, and this action can be studied using GKM theory. We prove two results about this manifold and its GKM graph. The first theorem describes how the GKM graph of $Q_{Γ, λ}$ is obtained from the GKM graph of the corresponding manifold $M_{Γ, λ}$ of isospectral Hermitian matrices. The second theorem gives a criterion for equivariant formality of $Q_{Γ, λ}$. |
| title | GKM Theory for Manifolds of Isospectral Matrices in Lie Type D |
| topic | Algebraic Topology Combinatorics 15B57, 57R91, 57S12, 14M15, 55N91 (Primary) 57R19, 15A18, 57S25, 05C25, 05C76, 15B30, 17B99 (Secondary) |
| url | https://arxiv.org/abs/2602.08366 |