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On the Finite W-Algebra for the Queer Lie Superalgebra

  • Elena PoletaevaEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 277)

Abstract

In this paper, we study the finite W-algebra \(W_{\chi }\) for the queer Lie superalgebra \({\mathfrak {g}= Q(N)}\) associated with an arbitrary even nilpotent element \(\chi \) in the coadjoint representation. We describe the annihilator \({\mathfrak {g}^{\chi }}\) and construct a set of elements in the generalized Whittaker module \({U(\mathfrak {g})/I_{\chi }}\) which under certain map project onto a homogeneous basis in \({\mathfrak {g}^{\chi }}\). In the case when the corresponding nilpotent element has Jordan blocks of equal size, these elements form a set of generators for \(W_{\chi }\).

Keywords

Finite W-algebra Queer Lie superalgebra Kazhdan filtration 

Notes

Acknowledgements

This work was supported by a grant from the Simons Foundation (#354874, Elena Poletaeva). I thank V. Serganova and V. Stukopin for very helpful discussions.

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Authors and Affiliations

  1. 1.School of Mathematical and Statistical Sciences, University of Texas Rio Grande ValleyEdinburgUSA

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