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Acta Mathematica Vietnamica

, Volume 44, Issue 3, pp 603–615 | Cite as

Jacobi-Trudi Type Formula for Character of Irreducible Representations of \(\frak {gl}(m|1)\)

  • Nguyên Luong Thái Bình
  • Nguyên Thi Phuong Dung
  • Phùng Hô HaiEmail author
Article

Abstract

We prove a determinantal type formula to compute the irreducible characters of the general Lie superalgebra \(\mathfrak {gl}(m|1)\) in terms of the characters of the symmetric powers of the fundamental representation and their duals. This formula was conjectured by J. van der Jeugt and E. Moens for the Lie superalgebra \(\frak {gl}(m|n)\) and generalizes the well-known Jacobi-Trudi formula.

Keywords

Character formula Jacobi-trudi type formula Character formula of Lie superalgebra 

Mathematics Subject Classification (2010)

17B10 17B15 17B20 17B22 

Notes

Acknowledgements

The authors would like to thank VIASM for the financial support and the excellent working environment.

Funding Information

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED), grant number 101.04-2016.19. A part of this work was carried out when the first and the third named authors were visiting the Vietnam Institute for Advanced Study in Mathematics.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Nguyên Luong Thái Bình
    • 1
  • Nguyên Thi Phuong Dung
    • 2
  • Phùng Hô Hai
    • 3
    Email author
  1. 1.Sai Gon UniversityHo Chi Minh CityVietnam
  2. 2.Banking AcademyHanoiVietnam
  3. 3.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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