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The Ramanujan Journal

, Volume 7, Issue 4, pp 519–530 | Cite as

Addendum to ‘Bosonic Formulas for (k, l)-Admissible Partitions’

  • B. Feigin
  • M. Jimbo
  • S. Loktev
  • T. Miwa
  • E. Mukhin
Article

Abstract

In our previous paper we made a combinatorial study of (k, l)-admissible partitions. This object appeared already in the work of M. Primc as a label of a basis of level k-integrable modules over \(\widehat{\mathfrak{s}\mathfrak{l}}_l \). We clarify the relation between these two works. As a byproduct we obtain an explicit parameterization of the affine Weyl group of \(\widehat{\mathfrak{s}\mathfrak{l}}_l \) by a simple combinatorial set.

q-series q-difference equation admissible partitions 

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References

  1. 1.
    B. Feigin, M. Jimbo, S. Loktev, T. Miwa, and E. Mukhin, “Bosonic formulas for (k, l)-admissible partitions,” Ramanujan Journal 7 (2003), 485–517.Google Scholar
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    B. Feigin and A. Stoyanovsky, “Quasi-particles models for the representations of Lie algebras and geometry of flag manifold,” hep-th/9308079, RIMS 942; “Functional models for the respresentations of current algebras and the semi-infinite Schubert cells,” Funct. Anal. Appl. 28 (1994), 55–72.Google Scholar
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    V. Kac, Infnite-Dimensional Lie Algebras, 3rd edn., Cambridge University Press, 1990.Google Scholar
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    M. Primc, “Vertex operator construction of standard modules for A n(1),” Pacific J. Math. 162 (1994) 143–187; “Standard representations of A n(1),” in Proceedings of Marseilles Conference 'Infinite Dimensional Lie Algebras and Groups', Advanced Studies in Mathematical Physics, World Scientific, Singapore, 7 (1988), 273-282.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • B. Feigin
    • 1
  • M. Jimbo
    • 2
  • S. Loktev
    • 3
  • T. Miwa
    • 4
  • E. Mukhin
    • 5
  1. 1.Landau Institute for Theoretical PhysicsChernogolovkaRussia
  2. 2.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan
  3. 3.Institute for Theoretical and Experemental Physics andIndependent University of MoscowRussia
  4. 4.Division of Mathematics, Graduate School of ScienceKyoto UniversityKyotoJapan
  5. 5.Department of MathematicsIndiana University-Purdue University-IndianapolisIndianapolis

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