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Characters and composition factor multiplicities for the Lie superalgebra gl(m/n)

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J. Van der Jeugt, R.B. Zhang

Representation Theory · Submitted 4 Nov 1998

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

The authors' main claim In particular, we claim that for an r-fold atypical weight mu there are 2^r distinct weights lambda such that a_{lambda,mu}=1, and a_{lambda,mu}=0 for all other weights lambda.

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arXiv IDmath/9811015 (version 1)
Pith IDTI2XM2I6, Pith's permanent record of this paper and its review
CitationJ. Van der Jeugt, R.B. Zhang. "Characters and composition factor multiplicities for the Lie superalgebra gl(m/n)." arXiv:math/9811015 (1998). https://pith.science/paper/TI2XM2I6
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,066 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.57 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.89 · mentions code or data availability 0.02.

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

The multiplicities a_{lambda,mu} of simple modules L(mu) in the composition series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character problem for gl(m/n). In Serganova's algorithm all mu with nonzero a_{lambda,mu} are determined for a given lambda; this algorithm turns out to be rather complicated. In this Letter a simple rule is conjectured to find all nonzero a_{lambda,mu} for any given weight mu. In particular, we claim that for an r-fold atypical weight mu there are 2^r distinct weights lambda such that a_{lambda,mu}=1, and a_{lambda,mu}=0 for all other weights lambda. Some related properties on the multiplicities a_{lambda,mu} are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan-Lusztig polynomials is discussed.

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 The multiplicities a_{lambda,mu} of simple modules L(mu) in the composition series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character problem for gl(m/n). background 1.00 0.03 0.06 asserted 1.00
s1 In Serganova's algorithm all mu with nonzero a_{lambda,mu} are determined for a given lambda; this algorithm turns out to be rather complicated. background 0.82 0.26 0.02 asserted 0.99
s2 In this Letter a simple rule is conjectured to find all nonzero a_{lambda,mu} for any given weight mu. contribution 0.99 0.80 0.28 speculative 0.93
s3 In particular, we claim that for an r-fold atypical weight mu there are 2^r distinct weights lambda such that a_{lambda,mu}=1, and a_{lambda,mu}=0 for all other weights lambda. result 0.70 0.75 0.87 asserted 0.51
s4 Some related properties on the multiplicities a_{lambda,mu} are proved, and arguments in favour of our main conjecture are given. contribution 0.81 0.92 0.07 asserted 0.99
s5 Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan-Lusztig polynomials is discussed. contribution 0.51 0.79 0.05 unclear 0.54

What kind of paper the classifier reports this is: theoretical result 0.77 · evidence from argument 0.58.

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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

The multiplicities a_{lambda,mu} of simple modules L(mu) in the composition series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character problem for gl(m/n). In Serganova's algorithm all mu with nonzero a_{lambda,mu} are determined for a given lambda; this algorithm turns out to be rather complicated. In this Letter a simple rule is conjectured to find all nonzero a_{lambda,mu} for any given weight mu. In particular, we claim that for an r-fold atypical weight mu there are 2^r distinct weights lambda such that a_{lambda,mu}=1, and a_{lambda,mu}=0 for all other weights lambda. Some related properties on the multiplicities a_{lambda,mu} are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan-Lusztig polynomials is discussed.

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