Weight strings in nonstandard representations of Kac-Moody algebras

Dillon, Meighan I.

doi:10.1090/S0002-9947-1990-0964898-9

Weight strings in nonstandard representations of Kac-Moody algebras
HTML articles powered by AMS MathViewer

by Meighan I. Dillon

Trans. Amer. Math. Soc. 320 (1990), 161-169

DOI: https://doi.org/10.1090/S0002-9947-1990-0964898-9

PDF | Request permission

Abstract:

We consider the weights which occur in arbitrary irreducible highest weight representations of Kac-Moody algebras and determine conditions under which certain weights may or may not occur.

References

I. B. Frenkel, Representations of Kac-Moody algebras and dual resonance models, Applications of group theory in physics and mathematical physics (Chicago, 1982) Lectures in Appl. Math., vol. 21, Amer. Math. Soc., Providence, RI, 1985, pp. 325–353. MR 789298
I. B. Frenkel, Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory, J. Functional Analysis 44 (1981), no. 3, 259–327. MR 643037, DOI 10.1016/0022-1236(81)90012-4
I. B. Frenkel and V. G. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980/81), no. 1, 23–66. MR 595581, DOI 10.1007/BF01391662
James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842
Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
Victor G. Kac, Infinite-dimensional Lie algebras, Progress in Mathematics, vol. 44, Birkhäuser Boston, Inc., Boston, MA, 1983. An introduction. MR 739850, DOI 10.1007/978-1-4757-1382-4

Simple irreducible graded Lie algebras of finite growth

2

V. G. Kac, D. A. Kazhdan, J. Lepowsky, and R. L. Wilson, Realization of the basic representations of the Euclidean Lie algebras, Adv. in Math. 42 (1981), no. 1, 83–112. MR 633784, DOI 10.1016/0001-8708(81)90053-0
Victor G. Kac and Dale H. Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms, Adv. in Math. 53 (1984), no. 2, 125–264. MR 750341, DOI 10.1016/0001-8708(84)90032-X
J. Lepowsky, Some constructions of the affine Lie algebra $A^{(1)}_1$, Applications of group theory in physics and mathematical physics (Chicago, 1982) Lectures in Appl. Math., vol. 21, Amer. Math. Soc., Providence, RI, 1985, pp. 375–397. MR 789300

Lectures on Kac-Moody algebras

David Mitzman, Integral bases for affine Lie algebras and their universal enveloping algebras, Contemporary Mathematics, vol. 40, American Mathematical Society, Providence, RI, 1985. MR 786830, DOI 10.1090/conm/040
Robert V. Moody, Euclidean Lie algebras, Canadian J. Math. 21 (1969), 1432–1454. MR 255627, DOI 10.4153/CJM-1969-158-2
R. V. Moody, Lie algebras associated with generalized Cartan matrices, Bull. Amer. Math. Soc. 73 (1967), 217–221. MR 207783, DOI 10.1090/S0002-9904-1967-11688-4
Robert V. Moody, A new class of Lie algebras, J. Algebra 10 (1968), 211–230. MR 229687, DOI 10.1016/0021-8693(68)90096-3
Robert Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335