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pith:CU7IL5EO

pith:2026:CU7IL5EOZHHC4WANFT6FOQASSB

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Temperley-Lieb Immanants of Ribbon Decomposition Matrices

Pavlo Pylyavskyy, Son Nguyen

Temperley-Lieb immanants evaluate to Schur-positive polynomials on ribbon decomposition matrices.

arxiv:2605.12880 v1 · 2026-05-13 · math.CO · math.RT

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Claims

C1strongest claim

We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices.

C2weakest assumption

The ribbon decomposition matrices and the Temperley-Lieb immanants satisfy the combinatorial and algebraic properties needed for the positivity evaluation to hold as stated, relying on definitions and prior results such as Haiman's for the special case.

C3one line summary

Temperley-Lieb immanants are Schur-positive on ribbon decomposition matrices, extending known Jacobi-Trudi cases, with a conjecture for the full dual canonical basis.

References

63 extracted · 63 resolved · 0 Pith anchors

[1] Remmel, J. B. and Whitney, R. , TITLE =. J. Algorithms , FJOURNAL =. 1984 , NUMBER =. doi:10.1016/0196-6774(84)90002-6 , URL = 1984 · doi:10.1016/0196-6774(84)90002-6

[2] Philosophical Transactions of the Royal Society of London 1934 · doi:10.1098/rsta.1934.0015

[3] Zelevinsky, A. V. , TITLE =. J. Algebra , FJOURNAL =. 1981 , NUMBER =. doi:10.1016/0021-8693(81)90128-9 , URL = 1981 · doi:10.1016/0021-8693(81)90128-9

[4] Berenstein, A. D. and Zelevinsky, A. V. , TITLE =. J. Algebraic Combin. , FJOURNAL =. 1992 , NUMBER =. doi:10.1023/A:1022429213282 , URL = 1992 · doi:10.1023/a:1022429213282

[5] Berenstein, Arkady and Zelevinsky, Andrei , TITLE =. Invent. Math. , FJOURNAL =. 2001 , NUMBER =. doi:10.1007/s002220000102 , URL = 2001 · doi:10.1007/s002220000102

Receipt and verification

First computed	2026-05-18T03:09:11.104794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

153e85f48ec9ce2e580d2cfc574012904d581c2ce41af2a1e7a236ae765f1dc6

Aliases

arxiv: 2605.12880 · arxiv_version: 2605.12880v1 · doi: 10.48550/arxiv.2605.12880 · pith_short_12: CU7IL5EOZHHC · pith_short_16: CU7IL5EOZHHC4WAN · pith_short_8: CU7IL5EO

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/CU7IL5EOZHHC4WANFT6FOQASSB \
  | 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: 153e85f48ec9ce2e580d2cfc574012904d581c2ce41af2a1e7a236ae765f1dc6

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T01:51:55Z",
    "title_canon_sha256": "665a072ccd31d979d95c0db4203f154625f014f5c0bd8a5c624deede3e43a834"
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