Glasnik Matematicki, Vol. 46, No.1 (2011), 49-70.

CHARACTERS OF FEIGIN-STOYANOVSKY'S TYPE SUBSPACES OF LEVEL ONE MODULES FOR AFFINE LIE ALGEBRAS OF TYPES Al(1) AND D4(1)

Goran Trupčević

Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
e-mail: gtrup@math.hr

Abstract.   We use combinatorial description of bases of Feigin-Stoyanovsky's type subspaces of standard modules of level 1 for affine Lie algebras of types Al(1) and D4(1) to obtain character formulas. These descriptions naturally lead to systems of recurrence relations for which we also find solutions.

2000 Mathematics Subject Classification.   17B67, 05A19.

Key words and phrases.   Affine Lie algebras, principal subspaces, character formulas.

Full text (PDF) (free access)

DOI: 10.3336/gm.46.1.08

References:

  1. I. Baranović, Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 2 standard modules for D4(1), math.QA/0903.0739.

  2. I. Baranović, in preparation.

  3. C. Calinescu, Intertwining vertex operators and certain representations of sl(n), Commun. Contemp. Math. 10 (2008), 47-79.
    MathSciNet     CrossRef

  4. C. Calinescu, Principal subspaces of higher-level standard sl(3)-modules, J. Pure Appl. Algebra 210 (2007), 559-575.
    MathSciNet     CrossRef

  5. C. Calinescu, J. Lepowsky and A. Milas, Vertex-algebraic structure of the principal subspaces of certain A1(1)-modules. I. Level one case, Int. J. Math. 19 (2008), 71-92.
    MathSciNet     CrossRef

  6. C. Calinescu, J. Lepowsky and A. Milas, Vertex-algebraic structure of the principal subspaces of certain A1(1)-modules. II. Higher level case, J. Pure Appl. Algebra 212 (2008), 1928-1950.
    MathSciNet     CrossRef

  7. C. Calinescu, J. Lepowsky and A. Milas, Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A, D, E, J. Algebra 323 (2010), 167-192.
    MathSciNet     CrossRef

  8. S. Capparelli, J. Lepowsky and A. Milas, The Rogers-Ramanujan recursion and intertwining operators, Commun. Contemp. Math. 5 (2003), 947-966.
    MathSciNet     CrossRef

  9. S. Capparelli, J. Lepowsky and A. Milas, The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators, Ramanujan J. 12 (2006), 379-397.
    MathSciNet     CrossRef

  10. B. Feigin, M. Jimbo, S. Loktev, T. Miwa and E. Mukhin, Bosonic formulas for (k,l)-admissible partitions, Ramanujan J. 7 (2003), 485-517.; Addendum to `Bosonic formulas for (k,l)-admissible partitions', Ramanujan J. 7 (2003), 519-530.
    MathSciNet     CrossRef
    MathSciNet     CrossRef

  11. B. Feigin, M. Jimbo, T. Miwa, E. Mukhin and Y. Takeyama, Fermionic formulas for (k,3)-admissible configurations, Publ. Res. Inst. Math. Sci. 40 (2004), 125-162.
    MathSciNet     CrossRef

  12. B. Feigin, M. Jimbo, T. Miwa, E. Mukhin and Y. Takeyama, Particle content of the (k,3)-configurations, Publ. Res. Inst. Math. Sci. 40 (2004), 163-220.
    MathSciNet     CrossRef

  13. A. V. Stoyanovsky and B. L. Feigin, Functional models of the representations of current algebras, and semi-infinite Schubert cells, (Russian) Funktsional. Anal. i Prilozhen. 28 (1994), 68-90, 96; translation in Funct. Anal. Appl. 28 (1994), 55-72.
    MathSciNet     CrossRef

  14. G. Georgiev, Combinatorial constructions of modules for infinite-dimensional Lie algebras. I. Principal subspace, J. Pure Appl. Algebra 112 (1996), 247-286.
    MathSciNet     CrossRef

  15. M. Jerković, Recurrence relations for characters of affine Lie algebra Al(1), J. Pure Appl. Algebra 213 (2009), 913-926.
    MathSciNet     CrossRef

  16. M. Jerković, Character formulas for Feigin-Stoyanovsky's type subspaces of standard sl(3, C)~-modules, arXiv:1105.2927v1 [math.QA].

  17. M. Jerković, Recurrence relations for characters of affine Lie algebra Al(1), PhD thesis, University of Zagreb, 2007.

  18. V. G. Kac, Infinite-dimensional Lie algebras. 3rd ed., Cambridge University Press, Cambridge, 1990.
    MathSciNet     CrossRef

  19. M. Primc, Vertex operator construction of standard modules for An(1), Pacific J. Math. 162 (1994), 143-187.
    MathSciNet     CrossRef

  20. M. Primc, Basic representations for classical affine Lie algebras, J. Algebra 228 (2000), 1-50.
    MathSciNet     CrossRef

  21. M. Primc, (k,r)-admissible configurations and intertwining operators, Contemp. Math. 442 (2007), 425-434.
    MathSciNet    

  22. G. Trupčević, Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 1 standard sl(l+1,C)-modules, Commun. Algebra 38 (2010), 3913-3940.
    MathSciNet     CrossRef

  23. G. Trupčević, Combinatorial bases of Feigin-Stoyanovsky's type subspaces of higher-level standard sl(l+1,C)-modules, J. Algebra 322 (2009), 3744-3774.
    MathSciNet     CrossRef
Glasnik Matematicki Home Page