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NON-STANDARD VERMA TYPE MODULES FOR 𝔮(n)(2)

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Abstract

We study non-standard Verma type modules over the Kac-Moody queer Lie superalgebra 𝔮(n)(2). We give a sufficient condition under which such modules are irreducible. We also give a classification of all irreducible diagonal ℤ-graded modules over certain Heisenberg Lie superalgebras contained in 𝔮(n)(2).

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References

  1. [BBFK13]

    V. Bekkert, G. Benkart, V. Futorny, I. Kashuba, New irreducible modules for Heisenberg and affine Lie algebras, J. Algebra 373 (2013), 284–298.

  2. [CF18]

    L. Calixto, V. Futorny, Highest weight modules for affine Lie superalgebras, arXiv:1804.02563 (2018).

  3. [Cox94]

    B. Cox, Verma modules induced from nonstandard Borel subalgebras, Pacific J. Math. 165 (1994), no. 2, 269–294.

  4. [DFG09]

    I. Dimitrov, V. Futorny, D. Grantcharov, Parabolic sets of roots, in: Groups, Rings and Group Rings, Contemp. Math., Vol. 499, Amer. Math. Soc., Providence, RI, 2009, pp. 61–73.

  5. [ERF09]

    S. Eswara Rao, V. Futorny, Integrable modules for affine Lie superalgebras, Trans. Amer. Math. Soc. 361 (2009), no. 10, 5435–5455.

  6. [Fut94]

    V. Futorny, Imaginary Verma modules for affine Lie algebras, Canad. Math. Bull. 37 (1994), no. 2, 213–218.

  7. [Fut97]

    V. Futorny, Representations of Affine Lie Algebras, Queen’s Papers in Pure and Applied Mathematics, 106. Queen’s University, Kingston, ON, 1997.

  8. [GS08]

    M. Gorelik, V. Serganova, On representations of the affine superalgebra 𝔮(n)(2), Mosc. Math. J. 8 (2008), no. 1, 91–109, 184.

  9. [HS07]

    C. Hoyt, V. Serganova, Classification of finite-growth general Kac-Moody superalgebras, Comm. Algebra 35 (2007), no. 3, 851–874.

  10. [Kac77]

    V. Kac, Lie superalgebras, Adv. Math. 26 (1977), no. 1, 8–96.

  11. [Ser11]

    V. Serganova, Kac-Moody superalgebras and integrability, in: Developments and Trends in Infinite-dimensional Lie Theory, Progress in Mathematics, Vol. 288, Birkhäuser Boston, Boston, MA, 2011, pp. 169–218.

  12. [vdL89]

    J. W. van de Leur, A classification of contragredient Lie superalgebras of finite growth, Comm. Algebra 17 (1989), no. 8, 1815–1841.

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Correspondence to L. CALIXTO.

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Supported by the CNPq grant (200783/2018-1).

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CALIXTO, L., FUTORNY, V. NON-STANDARD VERMA TYPE MODULES FOR 𝔮(n)(2). Transformation Groups (2020). https://doi.org/10.1007/s00031-020-09550-y

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