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

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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.

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Acknowledgements

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

Funding

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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Authors and Affiliations

  1. Sai Gon University, Ho Chi Minh City, Vietnam

    Nguyên Luong Thái Bình

  2. Banking Academy, Hanoi, Vietnam

    Nguyên Thi Phuong Dung

  3. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Phùng Hô Hai

Authors
  1. Nguyên Luong Thái Bình
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  2. Nguyên Thi Phuong Dung
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  3. Phùng Hô Hai
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Corresponding author

Correspondence to Phùng Hô Hai.

Additional information

Dedicated to Professor Lê Tuân Hoa on the occasion of his sixtieth birthday

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Bình, N.L.T., Dung, N.T.P. & Hai, P.H. Jacobi-Trudi Type Formula for Character of Irreducible Representations of \(\frak {gl}(m|1)\). Acta Math Vietnam 44, 603–615 (2019). https://doi.org/10.1007/s40306-018-0280-1

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  • DOI: https://doi.org/10.1007/s40306-018-0280-1

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