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pith:WTCHQMDN

pith:2026:WTCHQMDNBRM6I3UNCQBB7FMBDQ

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Non-combinatorial involutive braidings: the quantum algebra $\mathfrak{gl}_{k,m}$

Anastasia Doikou

Involutive non-combinatorial solutions of the braid equation define the gl_{k,m} Yangian as a subalgebra whose highest-weight modules diagonalize quantum spin-chain Hamiltonians.

arxiv:2605.16121 v1 · 2026-05-15 · math.QA · math-ph · math.MP · math.RT

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Claims

C1strongest claim

By employing these solutions, we identify the associated quantum algebra, which we introduce as the gl_{k,m} Yangian. The algebra gl_{k,m} is also recognized as a subalgebra of the Yangian. Furthermore, we construct specific highest-weight modules of gl_{k,m}, which simultaneously yield the eigenstates of certain quantum spin-chain-like Hamiltonians.

C2weakest assumption

The involutive non-combinatorial solutions of the braid equation can be viewed as special deformations of the permutation map in a way that consistently produces a well-defined quantum algebra structure and its highest-weight modules without internal contradictions.

C3one line summary

Defines the gl_{k,m} Yangian as a subalgebra of the Yangian from non-combinatorial braid solutions and constructs its highest-weight modules as eigenstates of associated spin-chain Hamiltonians, reducing to a Heisenberg XX variant for gl_{1,1}.

References

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[1] Baxter,Exactly solved models in statistical mechanics, Academic Press (1982) 1982

[2] A. Berele and A. Regev,Hook Young diagrams, combinatorics and representations of Lie superalgebras, Bull. Amer. Math. Soc. (N.S.), 8(2) (1983) 337–339 1983

[3] N. Cramp´ e, R. Nepomechie, L. Vinet and N. Zare Harofteh,su(2)symmetry of XX spin chains, Math. Phys. Analysis and Geometry (2026) 29:3 2026

[4] A. Doikou and P.P. Martin,Hecke algebraic approach to the reflection equation for spin chains, J. Phys. A36 (2003) 2203-2226 2003

[5] Doikou,From affine Hecke algebras to boundary symmetries, Nucl.Phys 2005

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Receipt and verification

First computed	2026-05-20T00:01:53.739408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4c478306d0c59e46e8d14021f95811c19cea387b57ade71b0e6e5d87fa3a244

Aliases

arxiv: 2605.16121 · arxiv_version: 2605.16121v1 · doi: 10.48550/arxiv.2605.16121 · pith_short_12: WTCHQMDNBRM6 · pith_short_16: WTCHQMDNBRM6I3UN · pith_short_8: WTCHQMDN

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/WTCHQMDNBRM6I3UNCQBB7FMBDQ \
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# expect: b4c478306d0c59e46e8d14021f95811c19cea387b57ade71b0e6e5d87fa3a244

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-05-15T16:05:32Z",
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