Pith Number

pith:SOCSHI25

pith:2026:SOCSHI25B6NJ5CEAGLWIOZOLER

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Asymptotic Vanishing of Stiefel--Whitney Classes for $\mathrm{GL}_n(\mathbb{F}_q)$

Anwesh Ray

For fixed odd q, as n grows the proportion of irreducible orthogonal representations of GL_n(F_q) with trivial first and second Stiefel-Whitney classes tends to 1.

arxiv:2604.27235 v2 · 2026-04-29 · math.RT · math.AT · math.GR · math.NT

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Claims

C1strongest claim

For fixed odd q, we show that as n → ∞, the values of irreducible orthogonal characters become highly divisible by powers of 2 for almost all representations. As a consequence, the proportion of irreducible orthogonal representations with trivial first and second Stiefel-Whitney classes tends to 1, and if q ≡ 1 (mod 4), the same holds for the fourth Stiefel-Whitney class.

C2weakest assumption

The recent formulas expressing Stiefel-Whitney classes in terms of character values at elements of order dividing 2 are valid and applicable to irreducible orthogonal representations of GL_n(F_q), allowing the reduction of class vanishing to 2-adic divisibility questions.

C3one line summary

As n tends to infinity with q fixed and odd, the proportion of irreducible orthogonal representations of GL_n(F_q) with trivial first and second Stiefel-Whitney classes approaches 1, with similar behavior for the fourth class when q ≡ 1 mod 4.

Receipt and verification

First computed	2026-05-26T01:03:31.376380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

938523a35d0f9a9e888032ec8765cb2476e77da272e01b35a4a41ae468ab5195

Aliases

arxiv: 2604.27235 · arxiv_version: 2604.27235v2 · doi: 10.48550/arxiv.2604.27235 · pith_short_12: SOCSHI25B6NJ · pith_short_16: SOCSHI25B6NJ5CEA · pith_short_8: SOCSHI25

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SOCSHI25B6NJ5CEAGLWIOZOLER \
  | 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: 938523a35d0f9a9e888032ec8765cb2476e77da272e01b35a4a41ae468ab5195

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca7e3a0a8b05c80571188f522031fc909019641b9edc3d849c058227d6075e7f",
    "cross_cats_sorted": [
      "math.AT",
      "math.GR",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-04-29T22:15:45Z",
    "title_canon_sha256": "c25e1824a8218b493895c2681a50eca911efc0e7f0f6f461279f6cfe9f6de076"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.27235",
    "kind": "arxiv",
    "version": 2
  }
}