Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Corrigendum to "Representation stability for diagram algebras" [J. Algebra 638 (2024) 625-669]

Peter Patzt

Abstract

After the publication of [J. Algebra 638 (2024) 625-669], we noticed a serious mistake in the treatment of the partition algebra. In particular, we assumed in the proof of Lemma 4.9 that the trivial P_n-module is indexed by the empty set but it is actually indexed by the partition (n). In this erratum, we fix this mistake and give a complete proof of Theorem C.

Corrigendum to "Representation stability for diagram algebras" [J. Algebra 638 (2024) 625-669]

Abstract

After the publication of [J. Algebra 638 (2024) 625-669], we noticed a serious mistake in the treatment of the partition algebra. In particular, we assumed in the proof of Lemma 4.9 that the trivial P_n-module is indexed by the empty set but it is actually indexed by the partition (n). In this erratum, we fix this mistake and give a complete proof of Theorem C.

Paper Structure

This paper contains 3 sections, 11 theorems, 32 equations.

Table of Contents

  1. Background on Kronecker Coefficients
  2. Stability of reduced Kronecker coefficients
  3. Corrected proofs

Key Result

Theorem C

Under the assumption that $R = \mathbb C$ and $\delta\in \mathbb C\setminus\mathbb N$, a finitely presented $\mathcal{C}_{\mathop{\mathrm{P}}\nolimits}$-module gives rise to a representation stable sequence of representations of the partition algebras.

Theorems & Definitions (19)

  • Theorem C
  • Definition 1
  • Remark 1
  • Theorem 1: BDVO
  • Corollary 1: jameskerber
  • Corollary 2: Lit
  • Corollary 3: BDVO
  • Lemma 1
  • proof
  • Proposition 1
  • ...and 9 more