Abstract
Let G = GL(m|n) be a general linear supergroup, and Gev be its even subsupergroup isomorphic to GL(m) ×GL(n). In this paper, we use the explicit description of Gev-primitive vectors in the costandard supermodule ∇(λ), the largest polynomial G-subsupermodule of the induced supermodule \({H^{0}_{G}}(\lambda )\), for (m|n)-hook partition λ, and properties of certain morphisms ψk to derive results related to odd linkage for G over a field F of characteristic different from 2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Berele, A., Regev, A.: Hook Young diagrams with applications to combinatorics and to representations of Lie superalgabras. Adv. Math. 64, 118–175 (1987)
Brundan, J., Kujawa, J.: A new proof of the Mullineux conjecture. J. Algebraic Combin. 18(1), 13–39 (2003)
Grishkov, A.N., Marko, F.: Description of simple modules for Schur superalgebra S(2|2). Glasg. Math. J. 55(3), 695–719 (2013)
La Scala, R., Zubkov, A.N.: Costandard modules over Schur superalgebras in characteristic p. J. Algebra and its Appl. 7(2), 147–166 (2008)
van Leeuwen, M.A.A.: Tableau algorithms defined naturally for pictures. Discrete Math. 157(1-3), 321–362 (1996)
Marko, F.: Description of costandard modules of Schur superalgebra S(3|1). Comm. Algebra 41(7), 2665–2697 (2013)
Marko, F.: Primitive vectors in induced supermodules for general linear supergroups. J. Pure Appl. Algebra 219(4), 978–1007 (2015)
Marko, F.: Even-primitive vectors in induced supermodules for general linear supergroups and costandard supermodules for Schur superalgebras. J. Algebraic Combin. 51, 369–417 (2020)
Marko, F., Zubkov, A.N.: Blocks for general linear supergroup GL(m|n). Transform. Groups 23(1), 185–215 (2018)
Zelevinsky, A.V.: A generalization of the Littlewood-Richardson rule and the Richardson-Schensted-Knuth correspondence. J. Algebra 69(1), 82–94 (1981)
Zubkov, A.N.: Some properties of general linear supergroups and of Schur superalgebras. Algebra Logic 45(3), 147–171 (2006)
Acknowledgments
The author thanks an anonymous referee for careful reading of the manuscript and for suggesting improvements that increased its readability.
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented by: Henning Krause
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Marko, F. Combinatorial Aspects of An Odd Linkage Property for General Linear Supergroups. Algebr Represent Theor 25, 1429–1460 (2022). https://doi.org/10.1007/s10468-021-10073-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10468-021-10073-7