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The Ramanujan Journal

, Volume 45, Issue 1, pp 265–289 | Cite as

Bases of Feigin–Stoyanovsky’s type subspaces for \(C_\ell ^{(1)}\)

  • Ivana Baranović
  • Mirko Primc
  • Goran TrupčevićEmail author
Article

Abstract

In this paper, we construct combinatorial bases of Feigin–Stoyanovsky’s type subspaces of standard modules for level k affine Lie algebra \(C_\ell ^{(1)}\). We prove spanning by using annihilating field \(x_\theta (z)^{k+1}\) of standard modules. In the proof of linear independence, we use simple currents and intertwining operators whose existence is given by fusion rules.

Keywords

Affine Lie algebras Combinatorial bases Principal subspace Intertwining operators Simple current 

Mathematics Subject Classification

17B67 17B69 05A19 

Notes

Acknowledgments

We are grateful to Dražen Adamović and Alex Feingold for useful information and stimulating discussions on fusion rules and intertwining operators.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Ivana Baranović
    • 1
  • Mirko Primc
    • 2
  • Goran Trupčević
    • 3
    Email author
  1. 1.Faculty of Chemical Engineering and TechnologyUniversity of ZagrebZagrebCroatia
  2. 2.Department of Mathematics, Faculty of ScienceUniversity of ZagrebZagrebCroatia
  3. 3.Faculty of Teacher EducationUniversity of ZagrebZagrebCroatia

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