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arxiv: 2606.27707 · v1 · pith:6OPYH6QAnew · submitted 2026-06-26 · 🧮 math.RT

The representations of the Lie superalgebra p(3) in characteristic 3

Ye Ren This is my paper

Pith reviewed 2026-06-29 02:39 UTC · model grok-4.3

classification 🧮 math.RT
keywords Lie superalgebrap(3)representationscharacteristic 3irreducible modulescharacter formulaemodular representations
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The pith

All irreducible modules of the Lie superalgebra p(3) in characteristic 3 are classified with explicit character formulae.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper classifies every irreducible module of the Lie superalgebra p(3) of rank 2 over an algebraically closed field of characteristic 3. It supplies character formulae for each of these modules. A sympathetic reader cares because the result finishes the description of simple representations for this specific superalgebra when the characteristic is 3. With the full list in hand, one can compute dimensions and other invariants for all irreducibles without further case-by-case work.

Core claim

Let g be the Lie superalgebra p(3) of rank 2 over an algebraically closed field K of characteristic p=3. We classify all irreducible modules of g, and give the character formulae for irreducible modules.

What carries the argument

The complete list of irreducible g-modules together with their character formulae

Load-bearing premise

The algebraic methods used succeed in locating every irreducible module without omissions.

What would settle it

An explicit irreducible module for p(3) in characteristic 3 whose character does not match any formula in the classification.

read the original abstract

Let $g$ be the Lie superalgebra $p(3)$ of rank 2 over an algebraically closed field $K$ of characteristic $p=3$. We classify all irreducible modules of $g$, and give the character formulae for irreducible modules.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript claims to classify all irreducible modules of the Lie superalgebra p(3) of rank 2 over an algebraically closed field of characteristic 3 and to provide character formulae for these modules.

Significance. A complete, verified classification for this low-rank case in positive characteristic would be a useful data point for the representation theory of exceptional Lie superalgebras, but the supplied text consists only of the abstract and contains no derivations, explicit module lists, or verification steps.

major comments (1)
  1. Abstract: the classification result is asserted without any derivation, explicit list of modules, or verification steps; without the full text it is impossible to check whether the claimed classification is supported by the arguments.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for reviewing our manuscript on the representations of the Lie superalgebra p(3) in characteristic 3. We address the concern about the lack of supporting material in the supplied text.

read point-by-point responses

  1. Referee: Abstract: the classification result is asserted without any derivation, explicit list of modules, or verification steps; without the full text it is impossible to check whether the claimed classification is supported by the arguments.

    Authors: The full manuscript contains the complete classification of all irreducible modules for p(3) over an algebraically closed field of characteristic 3, including explicit module constructions, derivations of irreducibility, and the associated character formulae. The provided text in the review appears to have been limited to the abstract; the body of the paper supplies the detailed arguments, lists, and verifications supporting the main theorem. We are prepared to resubmit the complete document if an error occurred in transmission. revision: no

Circularity Check

0 steps flagged

No significant circularity

full rationale

The abstract states a classification result and character formulae for irreducible modules of p(3) in char 3 but contains no equations, derivations, self-citations, or load-bearing steps. No derivation chain is present to inspect, so no reduction to inputs by construction or self-citation can be exhibited. The paper's central claim is a standard classification statement whose validity is independent of any circular mechanism in the given text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no specific free parameters, axioms, or invented entities can be extracted or verified from the manuscript.

pith-pipeline@v0.9.1-grok · 5550 in / 981 out tokens · 38729 ms · 2026-06-29T02:39:34.138723+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

14 extracted references · 2 canonical work pages

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