Weight multiplicity polynomials for affine Kac-Moody algebras of type A r

Georgia Benkart; Seok-Jin Kang; Kailash C. Misra

Compositio Mathematica (1996)

  • Volume: 104, Issue: 2, page 153-187
  • ISSN: 0010-437X

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Benkart, Georgia, Kang, Seok-Jin, and Misra, Kailash C.. "Weight multiplicity polynomials for affine Kac-Moody algebras of type $A_r$." Compositio Mathematica 104.2 (1996): 153-187. <http://eudml.org/doc/90485>.

@article{Benkart1996,
author = {Benkart, Georgia, Kang, Seok-Jin, Misra, Kailash C.},
journal = {Compositio Mathematica},
keywords = {weight multiplicity polynomials; affine Kac-Moody algebras; degree; dominant weights; Kostka numbers},
language = {eng},
number = {2},
pages = {153-187},
publisher = {Kluwer Academic Publishers},
title = {Weight multiplicity polynomials for affine Kac-Moody algebras of type $A_r$},
url = {http://eudml.org/doc/90485},
volume = {104},
year = {1996},
}

TY - JOUR
AU - Benkart, Georgia
AU - Kang, Seok-Jin
AU - Misra, Kailash C.
TI - Weight multiplicity polynomials for affine Kac-Moody algebras of type $A_r$
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 104
IS - 2
SP - 153
EP - 187
LA - eng
KW - weight multiplicity polynomials; affine Kac-Moody algebras; degree; dominant weights; Kostka numbers
UR - http://eudml.org/doc/90485
ER -

References

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  1. [BBL] Benkart, G.M., Britten, D.J. and Lemire, F.W.: Stability in Modules for Classical Lie Algebras - A Constructive Approach, Memoir Amer. Math. Soc.430 (1990). Zbl0706.17003MR1010997
  2. [BKM] Benkart, G., Kang, S.-J. and Misra, K.C.: Graded Lie algebras of Kac-Moody type, Adv. in Math.97 (1993) 154-190. Zbl0854.17026MR1201842
  3. [BK] Benkart, G. and Kass, S.N.: Weight multiplicities for affine Kac-Moody algebras, Modem Trends in Lie Theory, Queen's Papers in Pure and Applied Math. 94, V. Futorny and D. Pollack eds. (1994) 1-12. Zbl0818.17027MR1281175
  4. [FH] Fulton, W. and Harris, J.: Representation Theory, A First Course, Graduate Texts in Mathematics129Springer-Verlag, New York (1991). Zbl0744.22001MR1153249
  5. [FK] Frenkel, I.B. and Kac, V.G.: Basic representations of affine Lie algebras and dual resonance models, Invent. Math.62 (1980) 23-66. Zbl0493.17010MR595581
  6. [FL] Feingold, A.J. and Lepowsky, J.: The Weyl-Kac character formula and power series identities, Adv. Math.29 (1978) 271-309. Zbl0391.17009MR509801
  7. [GL] Garland, H. and Lepowsky, J.: Lie algebra homology and the Macdonald-Kac formulas, Invent. Math.34 (1976) 37-76. Zbl0358.17015MR414645
  8. [H] Humphreys, J.E.: Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics9Springer-Verlag, New York (1972). Zbl0254.17004MR499562
  9. [Kc] Kac, V.G.: Infinite Dimensional Lie Algebras, Third Ed., Cambridge University Press, Cambridge (1990). Zbl0716.17022MR1104219
  10. [Kn1] Kang, S.-J.: Kac-Moody Lie algebras, spectral sequences, and the Witt formula, Trans. Amer. Math. Soc.339 (1993) 463—495. Zbl0794.17014
  11. [Kn2] Kang, S. -J.: Root multiplicities of Kac-Moody algebras, Duke Math. J.74 (1994) 635-666. Zbl0823.17031MR1277948
  12. [KMPS] Kass, S., Moody, R.V., Patera, J. and Slansky, R.: Affine Lie Algebras, Weight Multiplicities, and Branching Rules, Vols. I and II, Los Alamos Series in Basic and Applied Sciences, Univ. of Calif. Press, Berkeley, Los Angeles, Oxford (1990). Zbl0785.17028
  13. [L] Liu, L.-S.: Kostant's formula for Kac-Moody Lie algebras, J. Algebra149 (1992) 155-178. Zbl0779.17024MR1165205
  14. [M] Macdonald, I.G.: Symmetric Functions and Hall Polynomials2nd ed., Clarendon Press, Oxford (1995). Zbl0824.05059MR1354144

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