Pith Number

pith:3XUHSKNU

pith:2026:3XUHSKNUK6U4Q6NXQAFDLEHBKY

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Linear representations of manifolds

Ke Ye, Lek-Heng Lim, Rongbiao Thomas Wang

Linear representations of G-manifolds as matrix maps supply explicit minimal dimensions for Mostow-Palais equivariant embeddings.

arxiv:2605.14013 v1 · 2026-05-13 · math.DG · math.RT

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Claims

C1strongest claim

We will give explicit values for dim V and show that our bounds are sharp. Furthermore, our method is constructive, giving explicit expressions for these minimal-dimensional Mostow-Palais embeddings.

C2weakest assumption

That the newly defined linear representations of the G-manifold exist and can be chosen so that the induced map into the space of matrices produces a Mostow-Palais embedding whose dimension is controlled by the representation dimension.

C3one line summary

Linear representations of G-manifolds generalize group representations and deliver explicit sharp bounds for Mostow-Palais G-equivariant embeddings into finite-dimensional modules.

References

42 extracted · 42 resolved · 0 Pith anchors

[1] A. Altland and M. R. Zirnbauer. Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures.Phys. Rev. B, 55:1142–1161, Jan 1997 1997

[2] F. W. Anderson and K. R. Fuller.Rings and categories of modules, volume 13 ofGraduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1992 1992

[3] M. Bardestani, K. Mallahi-Karai, and H. Salmasian. Minimal dimension of faithful representations forp-groups. J. Group Theory, 19(4):589–608, 2016 2016

[4] E. Bierstone. Equivariant Gromov theory.Topology, 13:327–345, 1974 1974

[5] Bump.Lie groups, volume 225 ofGraduate Texts in Mathematics 2013

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:13.041479Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dde87929b457a9c879b7800a3590e1561f6b28b05f7b81e28b73f910163e9d86

Aliases

arxiv: 2605.14013 · arxiv_version: 2605.14013v1 · doi: 10.48550/arxiv.2605.14013 · pith_short_12: 3XUHSKNUK6U4 · pith_short_16: 3XUHSKNUK6U4Q6NX · pith_short_8: 3XUHSKNU

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3XUHSKNUK6U4Q6NXQAFDLEHBKY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: dde87929b457a9c879b7800a3590e1561f6b28b05f7b81e28b73f910163e9d86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdc43bca9e4e4e6e327d449b4373359401f72c0471c59d3e2ed8586903a72e1e",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-13T18:26:45Z",
    "title_canon_sha256": "b62b93b5e5a328b4e90182a81c98e008a461cdb2e6d2910b2a67676b79997bfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14013",
    "kind": "arxiv",
    "version": 1
  }
}