A. N. Sergeev, “The tensor algebra of the identity representation as a module over the Lie superalgebras $\mathfrak Gl(n,m)$ and $Q(n)$”, Math. USSR-Sb., 51:2 (1985), 419

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Mathematics of the USSR-Sbornik, 1985, Volume 51, Issue 2, Pages 419–427
DOI: https://doi.org/10.1070/SM1985v051n02ABEH002867 (Mi sm2029)

This article is cited in 133 scientific papers (total in 133 papers)

The tensor algebra of the identity representation as a module over the Lie superalgebras

$\mathfrak Gl(n,m)$ and

$Q(n)$

A. N. Sergeev

English version PDF (531 kB) Citations (133) Russian version article

References:

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DOI: https://doi.org/10.1070/SM1985v051n02ABEH002867

Abstract: Let

$T$ be the tensor algebra of the identity representation of the Lie superalgebras in the series

$\mathfrak Gl$ and

$Q$ . The method of Weyl is used to construct a correspondence between the irreducible representations (respectively, the irreducible projective representations) of the symmetric group and the irreducible

$\mathfrak Gl$ - (respectively,

$Q$ -) submodules of

$T$ . The properties of the representations are studied on the basis of this correspondence. A formula is given for the characters on the irreducible

$Q$ -submodules of

$T$ .
Bibliography: 8 titles.

Received: 22.04.1983

Bibliographic databases:

UDC: 512

MSC: Primary 17A70, 17B10; Secondary 15A72, 20C30

Language: English

Original paper language: Russian

Citation: A. N. Sergeev, “The tensor algebra of the identity representation as a module over the Lie superalgebras

$\mathfrak Gl(n,m)$ and

$Q(n)$ ”, Math. USSR-Sb., 51:2 (1985), 419–427

Citation in format AMSBIB

\Bibitem{Ser84}

\by A.~N.~Sergeev

\paper The tensor algebra of the identity representation as a~module over the Lie superalgebras $\mathfrak Gl(n,m)$ and~$Q(n)$

\jour Math. USSR-Sb.

\yr 1985

\vol 51

\issue 2

\pages 419--427

\mathnet{http://mi.mathnet.ru/eng/sm2029}

\crossref{https://doi.org/10.1070/SM1985v051n02ABEH002867}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=735715}

\zmath{https://zbmath.org/?q=an:0573.17002}

Linking options:

https://www.mathnet.ru/eng/sm2029

https://doi.org/10.1070/SM1985v051n02ABEH002867

https://www.mathnet.ru/eng/sm/v165/i3/p422

This publication is cited in the following 133 articles:

Yaolong Shen, “Quantum supersymmetric pairs and ıSchur duality of type AIII”, Journal of Algebra, 661 (2025), 853
Santosha Pattanayak, Preena Samuel, “Graded picture invariants and polynomial invariants for mixed tensor superspaces”, Journal of Algebra, 661 (2025), 595
Jianmin Chen, Zhenhua Li, Hongying Zhu, “The braid group action on quantum queer superalgebra”, Journal of Algebra, 666 (2025), 169
Anton Alekseev, Florian Naef, Ján Pulmann, Pavol Ševera, “Batalin-Vilkovisky structures on moduli spaces of flat connections”, Advances in Mathematics, 443 (2024), 109580
Zhixiang Wu, “Some graded Hopf-module pseudoalgebras”, Journal of Algebra, 641 (2024), 587
A. P. Isaev, A. A. Provorov, “ $3$ -split Casimir operator of the $sl(M|N)$ and $osp(M|N)$ simple Lie superalgebras in the representation $\operatorname{ad}^{\otimes 3}$ and the Vogel parameterization”, Theoret. and Math. Phys., 221:1 (2024), 1726–1743
Jie Du, Haixia Gu, Zhenhua Li, Jinkui Wan, “Some Multiplication Formulas in Queer q-Schur Superalgebras”, Transformation Groups, 2024
E. N. Antonov, A. Yu. Orlov, “A new solvable two-matrix model and the BKP tau function”, Theoret. and Math. Phys., 217:3 (2023), 1807–1820
Deke Zhao, “Cyclotomic q-Schur superalgebras”, J. Algebra Appl., 22:10 (2023)
Yaroslav Drachov, Aleksandr Zhabin, “Genus expansion of matrix models and $\hbar$ expansion of BKP hierarchy”, Eur. Phys. J. C, 83:5 (2023)
VALENTIN BUCIUMAS, HANKYUNG KO, “POLYNOMIAL FUNCTORS AND TWO-PARAMETER QUANTUM SYMMETRIC PAIRS”, Transformation Groups, 28:1 (2023), 107
A. P. Isaev, A. A. Provorov, “Split Casimir operator and solutions of the Yang–Baxter equation for the $osp(M|N)$ and $s\ell(M|N)$ Lie superalgebras, higher Casimir operators, and the Vogel parameters”, Theoret. and Math. Phys., 210:2 (2022), 224–260
Kang Lu, “A note on odd reflections of super Yangian and Bethe ansatz”, Lett Math Phys, 112:2 (2022)
Haixia Gu, Zhenhua Li, Yanan Lin, “The integral Schur-Weyl-Sergeev duality”, Journal of Pure and Applied Algebra, 226:9 (2022), 107044
Shun-Jen Cheng, Kevin Coulembier, “Representation Theory of a Semisimple Extension of the Takiff Superalgebra”, International Mathematics Research Notices, 2022:18 (2022), 14454
A. Mironov, A. Morozov, A. Zhabin, “Spin Hurwitz theory and Miwa transform for the Schur Q-functions”, Physics Letters B, 829 (2022), 137131
Dmitry Chernyak, Sébastien Leurent, Dmytro Volin, “Completeness of Wronskian Bethe Equations for Rational ${\mathfrak {\mathfrak {gl}}_{{{\mathsf {m}}}|{{\mathsf {n}}}}}$ Spin Chains”, Commun. Math. Phys., 391:3 (2022), 969
Serge Skryabin, “On the graded algebras associated with Hecke symmetries, II. The Hilbert series”, J Algebr Comb, 56:1 (2022), 169
Jie Du, Yanan Lin, Zhongguo Zhou, “Quantum queer supergroups via υ-differential operators”, Journal of Algebra, 599 (2022), 48
A. Yu. Orlov, “Notes about the KP/BKP correspondence”, Theoret. and Math. Phys., 208:3 (2021), 1207–1227

Citing articles in Google Scholar: Russian citations, English citations
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