Pith Number

pith:JJWAQN5Y

pith:2026:JJWAQN5YV7LOCPREFXW6JDAYLL

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The category of Whittaker modules over the Cartan Type Lie algebra $\bar{S}_2$

Genqiang Liu, Xiaoyao Zheng, Yufang Zhao

Each block of Whittaker modules over the Cartan-type Lie algebra bar S_2 with finite-dimensional Whittaker vector spaces is equivalent to the finite-dimensional modules over its parabolic subalgebra bar S_2 to the non-negative part.

arxiv:2604.25185 v2 · 2026-04-28 · math.RT

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\pithnumber{JJWAQN5YV7LOCPREFXW6JDAYLL}

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Record completeness

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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

Each block Ω^{~S_2}_a of the category of (A_2, bar S_2)-Whittaker modules with finite-dimensional Whittaker vector spaces is equivalent to the finite-dimensional module category over the parabolic subalgebra bar S_2^{≥0}; all simple Whittaker bar S_2-modules with finite-dimensional Whittaker vector spaces are classified using gl_2-modules; and Ω^{bar S_2}_1 is equivalent to H_1-fmod.

C2weakest assumption

The Whittaker vector spaces are finite-dimensional; this restriction is essential for the block decomposition, the equivalences to parabolic and H_1 modules, and the classification via gl_2 to hold as stated.

C3one line summary

Blocks of Whittaker modules over bar S_2 with finite-dimensional Whittaker spaces are equivalent to finite-dimensional modules over a parabolic subalgebra, with simples classified via gl_2-modules and one block equivalent to H_1-fmod.

Receipt and verification

First computed	2026-06-19T16:12:20.385051Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a6c0837b8afd6e13e242dede48c185adc5e4c012698e051ce6bd7a9e2250b6b

Aliases

arxiv: 2604.25185 · arxiv_version: 2604.25185v2 · doi: 10.48550/arxiv.2604.25185 · pith_short_12: JJWAQN5YV7LO · pith_short_16: JJWAQN5YV7LOCPRE · pith_short_8: JJWAQN5Y

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JJWAQN5YV7LOCPREFXW6JDAYLL \
  | 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: 4a6c0837b8afd6e13e242dede48c185adc5e4c012698e051ce6bd7a9e2250b6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8087ff53b4d4d0af2290790cdbc614d9603e2a3800e41ca33313a4b58a8ab5c4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-04-28T03:43:53Z",
    "title_canon_sha256": "2d94206f8cfb7715051514f5ded3d2265d96c522ebc73164080e4a53f5e86599"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25185",
    "kind": "arxiv",
    "version": 2
  }
}