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Paper   IPM / M / 17081
School of Mathematics
  Title:   Representations of twisted affine Lie superalgebras–A recognition theorem
  Author(s):  Malihe Yousofzadeh
  Status:   Published
  Journal: J. Algebra
  Vol.:  609
  Year:  2022
  Pages:   407-436
  Supported by:  IPM
  Abstract:
Over the past three decades, representation theory of affine Lie (super)algebras has been a research spotlight in both areas Mathematics and Physics. The even part of almost all affine Lie superalgebras L contain two affine Lie algebras; say L0(1) and L0(2). Irreducible finite weight modules (f.w.m’s for short) are the first interesting class of modules over such an L. The structure of these modules strongly depends on whether of root vectors corresponding to real roots of L0(1) and L0(2) act locally nilpotently or not. we known that there is no nonzero irreducible f.w.m. of nonzero level over L for which root vectors corresponding to nonzero real roots of both L0(1) and L0(2) act locally nilpotently. This leads us to define quasi-integrable modules and study the case that root vectors corresponding to nonzero real roots of one of L0(1) and L0(2) act locally nilpotently. We give a recognition theorem for quasi-integrable modules over twisted affine Lie superalgebras.

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