Pith Number

pith:KEUFKEQZ

pith:2026:KEUFKEQZLFSF6HESMJZ4OEKBHV

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Orbits of subgroups of codimension one to four of the Iwahori group in the affine flag variety of $\text{SL}_2$

Claude Eicher

Finite-dimensional Schubert cells in the affine flag variety of SL₂ decompose into orbits under a chain of Iwahori subgroups of codimensions one to four.

arxiv:2605.13091 v1 · 2026-05-13 · math.AG

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3 Author claim open · sign in to claim

4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We describe how each finite dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits for a chain of subgroups of codimension one to four of the Iwahori group.

C2weakest assumption

The subgroups of the Iwahori group form a well-defined chain of codimensions one to four for which an explicit orbit decomposition exists on every finite-dimensional Schubert cell.

C3one line summary

Each finite-dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits under a chain of Iwahori subgroups of codimension one to four.

References

3 extracted · 3 resolved · 0 Pith anchors

[1] A. Beilinson and V. Drinfeld. Quantization of Hitchin 's integrable system and Hecke eigensheaves . Unpublished

[2] C. Eicher. Relaxed highest weight modules from D -modules on the Kashiwara flag scheme. https://arxiv.org/abs/1607.06342 arXiv:1607.06342 [math.RT] , 2016 2016

[3] C. Eicher. Twisted D -module extensions of local systems on a certain subvariety isomorphic to G _ m ^2 of the affine flag variety of SL _2 . https://arxiv.org/abs/2011.03764 arXiv:2011.03764 [math.AG 2011

Receipt and verification

First computed	2026-05-18T03:08:58.445137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

512855121959645f1c926273c711413d5081a7aade8f2dcf717fcc0dffe34602

Aliases

arxiv: 2605.13091 · arxiv_version: 2605.13091v1 · doi: 10.48550/arxiv.2605.13091 · pith_short_12: KEUFKEQZLFSF · pith_short_16: KEUFKEQZLFSF6HES · pith_short_8: KEUFKEQZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV \
  | 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: 512855121959645f1c926273c711413d5081a7aade8f2dcf717fcc0dffe34602

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8560eaa77d916c4359e9dac4a60eda05f887c260ef43d010121e497c51a2e86f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-13T07:01:53Z",
    "title_canon_sha256": "898aff74c9b24b67ff8f38812c6600142dc68bfb779daecad73b51bda5fe2ea1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13091",
    "kind": "arxiv",
    "version": 1
  }
}