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Quantum Schur Superalgebras and Kazhdan-Lusztig Combinatorics

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Jie Du, Hebing Rui

Quantum Algebra · Submitted 19 Oct 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this way, we classify all irreducible representations over $\mathbb Q(\up)$ via super-cell modules.

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arXiv ID1010.3800 (version 1)
Pith ID6OFHIJCA, Pith's permanent record of this paper and its review
CitationHebing Rui, Jie Du. "Quantum Schur Superalgebras and Kazhdan-Lusztig Combinatorics." arXiv:1010.3800 (2010). https://pith.science/paper/6OFHIJCA
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,691 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.54 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We introduce the notion of quantum Schur (or $q$-Schur) superalgebras. These algebras share certain nice properties with $q$-Schur algebras such as base change property, existence of canonical $\mathbb Z[v,v^{-1}]$-bases, and the duality relation with quantum matrix superalgebra $\sA(m|n)$. We also construct a cellular $\mathbb Q(\up)$-basis and determine its associated cells, called super-cells, in terms of a Robinson--Schensted--Knuth super-correspondence. In this way, we classify all irreducible representations over $\mathbb Q(\up)$ via super-cell modules.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We introduce the notion of quantum Schur (or $q$-Schur) superalgebras. contribution 1.00 0.95 0.08 asserted 0.99
s1 These algebras share certain nice properties with $q$-Schur algebras such as base change property, existence of canonical $\mathbb Z[v,v^{-1}]$-bases, and the duality relation with quantum matrix superalgebra $\sA(m|n)$. result 0.53 0.28 0.08 asserted 0.99
s2 We also construct a cellular $\mathbb Q(\up)$-basis and determine its associated cells, called super-cells, in terms of a Robinson--Schensted--Knuth super-correspondence. contribution 0.79 0.96 0.14 asserted 1.00
s3 In this way, we classify all irreducible representations over $\mathbb Q(\up)$ via super-cell modules. result 0.97 0.95 0.63 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • P abstract
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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We introduce the notion of quantum Schur (or $q$-Schur) superalgebras. These algebras share certain nice properties with $q$-Schur algebras such as base change property, existence of canonical $\mathbb Z[v,v^{-1}]$-bases, and the duality relation with quantum matrix superalgebra $\sA(m|n)$. We also construct a cellular $\mathbb Q(\up)$-basis and determine its associated cells, called super-cells, in terms of a Robinson--Schensted--Knuth super-correspondence. In this way, we classify all irreducible representations over $\mathbb Q(\up)$ via super-cell modules.

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1 arXiv paper cite this in 5 sentences

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