Realization of the level one standard $\tilde {C}_{2k+1}$-modules
HTML articles powered by AMS MathViewer
- by Kailash C. Misra PDF
- Trans. Amer. Math. Soc. 321 (1990), 483-504 Request permission
Abstract:
In this paper we study the level one standard (or irreducible integrable highest weight) modules for the affine symplectic Lie algebras. In particular, we give concrete realizations of all level one standard modules for the affine symplectic Lie algebras of even rank.References
- George E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. MR 0557013
- David M. Bressoud, Analytic and combinatorial generalizations of the Rogers-Ramanujan identities, Mem. Amer. Math. Soc. 24 (1980), no.ย 227, 54. MR 556608, DOI 10.1090/memo/0227
- Denis Bernard and Jean Thierry-Mieg, Level one representations of the simple affine Kac-Moody algebras in their homogeneous gradations, Comm. Math. Phys. 111 (1987), no.ย 2, 181โ246. MR 899850, DOI 10.1007/BF01217760
- I. B. Frenkel, Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory, J. Functional Analysis 44 (1981), no.ย 3, 259โ327. 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.ย 1, 23โ66. MR 595581, DOI 10.1007/BF01391662
- P. Goddard, W. Nahm, D. Olive, and A. Schwimmer, Vertex operators for non-simply-laced algebras, Comm. Math. Phys. 107 (1986), no.ย 2, 179โ212. MR 863639, DOI 10.1007/BF01209391
- Victor G. Kac, Infinite-dimensional Lie algebras, 2nd ed., Cambridge University Press, Cambridge, 1985. MR 823672
- Victor G. Kac and Dale H. Peterson, Spin and wedge representations of infinite-dimensional Lie algebras and groups, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no.ย 6, 3308โ3312. MR 619827, DOI 10.1073/pnas.78.6.3308
- Victor G. Kac and Dale H. Peterson, $112$ constructions of the basic representation of the loop group of $E_8$, Symposium on anomalies, geometry, topology (Chicago, Ill., 1985) World Sci. Publishing, Singapore, 1985, pp.ย 276โ298. MR 850863
- 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.ย 1, 83โ112. MR 633784, DOI 10.1016/0001-8708(81)90053-0 J. Lepowsky, Lectures on Kac-Moody Lie algebras, Universitรฉ Paris VI, Spring, 1978.
- J. Lepowsky, Calculus of twisted vertex operators, Proc. Nat. Acad. Sci. U.S.A. 82 (1985), no.ย 24, 8295โ8299. MR 820716, DOI 10.1073/pnas.82.24.8295
- James Lepowsky and Mirko Primc, Standard modules for type one affine Lie algebras, Number theory (New York, 1982) Lecture Notes in Math., vol. 1052, Springer, Berlin, 1984, pp.ย 194โ251. MR 750666, DOI 10.1007/BFb0071544
- James Lepowsky and Mirko Primc, Structure of the standard modules for the affine Lie algebra $A^{(1)}_1$, Contemporary Mathematics, vol. 46, American Mathematical Society, Providence, RI, 1985. MR 814303, DOI 10.1090/conm/046
- James Lepowsky and Robert Lee Wilson, Construction of the affine Lie algebra $A_{1}^{{}}(1)$, Comm. Math. Phys. 62 (1978), no.ย 1, 43โ53. MR 573075, DOI 10.1007/BF01940329
- James Lepowsky and Robert Lee Wilson, A new family of algebras underlying the Rogers-Ramanujan identities and generalizations, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no.ย 12, 7254โ7258. MR 638674, DOI 10.1073/pnas.78.12.7254
- James Lepowsky and Robert Lee Wilson, A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities, Adv. in Math. 45 (1982), no.ย 1, 21โ72. MR 663415, DOI 10.1016/S0001-8708(82)80012-1
- James Lepowsky and Robert Lee Wilson, The structure of standard modules. I. Universal algebras and the Rogers-Ramanujan identities, Invent. Math. 77 (1984), no.ย 2, 199โ290. MR 752821, DOI 10.1007/BF01388447
- James Lepowsky and Robert Lee Wilson, The structure of standard modules. II. The case $A^{(1)}_1$, principal gradation, Invent. Math. 79 (1985), no.ย 3, 417โ442. MR 782227, DOI 10.1007/BF01388515 M. Mandia, Structure of the level one standard modules for the affine Lie algebras $B_l^{(1)}$, $F_4^{(1)}$ and $G_2^{(1)}$, Mem. Amer. Math. Soc. 362 (1987).
- A. Meurman and M. Primc, Annihilating ideals of standard modules of $\textrm {sl}(2,\textbf {C})^\sim$ and combinatorial identities, Adv. in Math. 64 (1987), no.ย 3, 177โ240. MR 888628, DOI 10.1016/0001-8708(87)90008-9
- Kailash C. Misra, Structure of certain standard modules for $A^{(1)}_{n}$ and the Rogers-Ramanujan identities, J. Algebra 88 (1984), no.ย 1, 196โ227. MR 741940, DOI 10.1016/0021-8693(84)90098-X โ, Structure of some standard modules for $C_n^{(1)}$, J. Algebra 90 (1984), 384-409.
- Kailash C. Misra, Constructions of fundamental representations of symplectic affine Lie algebras, Topological and geometrical methods in field theory (Espoo, 1986) World Sci. Publ., Teaneck, NJ, 1986, pp.ย 147โ169. MR 1026487
- Kailash C. Misra, Realization of the level two standard $\textrm {sl}(2k+1,\textbf {C})^\sim$-modules, Trans. Amer. Math. Soc. 316 (1989), no.ย 1, 295โ309. MR 937880, DOI 10.1090/S0002-9947-1989-0937880-7
- Graeme Segal, Unitary representations of some infinite-dimensional groups, Comm. Math. Phys. 80 (1981), no.ย 3, 301โ342. MR 626704, DOI 10.1007/BF01208274
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 321 (1990), 483-504
- MSC: Primary 17B67; Secondary 17B10
- DOI: https://doi.org/10.1090/S0002-9947-1990-1005082-2
- MathSciNet review: 1005082