On Finite W-Algebras for Lie Superalgebras in the Regular Case

  • Elena Poletaeva
  • Vera Serganova
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 36)


We study finite W-algebras corresponding to the regular nilpotent orbits for classical Lie superalgebras of Type I. In the case when the Lie superalgebra has defect 1 we give a complete description of the finite W-algebras. We also present some partial results for the case \(\mathfrak{g}\mathfrak{l}(n\vert n)\) and formulate a general conjecture about the structure of these algebras.


Nilpotent Element Elementary Matrice Nilpotent Orbit Casimir Element Whittaker Vector 
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The authors would like to thank the Mathematisches Forschungsinstitut Oberwolfach for the hospitality and support in the spring of 2010. They also thank Crystal Hoyt for stimulating discussions and pointing out [1] and [3].

E.P. thanks the organizers of the 9-th International Workshop “Lie Theory and Its Applications in Physics” (LT-9), 20–26 June 2011, Varna, Bulgaria, for the very interesting conference and for the hospitality.


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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas-Pan AmericanEdinburgUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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