journal article Jul 01, 1985

Functional realizations of basis representations of factoring Lie groups and algebras

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References
22
[1]
V. G. Kac, "Infinite-dimensional Lie algebras," in: Progress in Mathematics, Vol. 44, Birkhäuser, Boston (1983).
[2]
I. V. Cherednik, "Determination of τ-functions for generalized affine Lie algebras," Funkts. Anal. Prilozhen.,17, No. 3, 93–95 (1983).
[3]
I. M. Gel'fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Theory of Representations and Automorphic Functions. Generalized Functions [in Russian], Vol. 6, Nauka, Moscow (1966).
[4]
Spin and wedge representations of infinite-dimensional Lie algebras and groups

Victor G. Kac, Dale H. Peterson

Proceedings of the National Academy of Sciences 1981 10.1073/pnas.78.6.3308
[5]
B. L. Feigin and D. V. Fuks, "Skew-symmetric invariant differential operators on the line and Verma modules over a Wirasoro algebra," Funkts. Anal. Prilozhen.,16, No. 2, 47–63 (1982).
[6]
E. Date, M. Jimbo, M. Kashiwara, and T. Miwa, "Operator approach to the Kadomtsev—Petviashvili equation. Transformation groups for soliton equations. III," J. Phys. Soc. Jpn.,50, 3806–3812 (1981). 10.1143/jpsj.50.3806
[7]
E. Date, M. Jimbo, M. Kashiwara, and T. Miwa, "Landau—Lifshitz equation: solitons, quasi-periodic solutions and infinite-dimensional Lie algebras," J. Phys. Soc. Jpn.,52, 388–393 (1983). 10.1143/jpsj.52.388
[8]
I. V. Cherednik, "Group interpretation of Baker functions and τ-functions," Usp. Mat. Nauk,38, No. 6, 133–134 (1983).
[9]
I. V. Cherednik, "Integrable differential equations and coverings of elliptic curves," Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 2, 183–205 (1983).
[10]
I. V. Cherednik, "Bäcklund—Darboux transformations for classical Yang—Baxter bundles," Funkts. Anal. Prilozhen.,17, No. 2, 88–89 (1983).
[11]
M. A. Semenov-Tyan-Shanskii, "What is a classical r-matrix?" Funkts. Anal. Prilozhen.,17, No. 4, 17–33 (1983).
[12]
A. A. Belavin and V. G. Drinfel'd, "Solutions of the classical Yang—Baxter equation for simple Lie algebras," Funkts. Anal. Prilozhen.,16, No. 3, 1–29 (1982).
[13]
M. Jimbo and T. Miwa, "Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II," Physica 2D, No. 3, 407–449 (1981).
[14]
A. G. Reiman and M. A. Semenov-Tjan-Shanskii, "Reduction of Hamiltonian systems, affine Lie algebras and Lax equations. II," Invent. Math.,63, 423–432 (1981). 10.1007/bf01389063
[15]
G. Segal and G. Wilson, "Loop groups and equations of KdV type," Preprint Math. Inst. Oxford Univ. (1983).
[16]
J. Lepowsky, "Lectures on Kac—Moody algebras," Preprint Univ. Paris VI, Paris (1978).
[17]
D. H. Peterson and V. G. Kac, "Infinite flag varieties and conjugacy theorems," Proc. Nat. Acad. Sci. USA,60, 1778–1782 (1983). 10.1073/pnas.80.6.1778
[18]
F. Bruhat and J. Tits, "Groupes reductifs sur un corps local. II," Preprint IHES, Paris (1983).
[19]
V. G. Drinfel'd and V. V. Sokolov, "Korteweg—de Vries type equations and simple Lie algebras," Dokl. Akad. Nauk SSSR,258, No. 1, 11–18 (1981).
[20]
J.-P. Serre, Algebraic groups and Class Fields [Russian translation], Mir, Moscow (1968).
[21]
L. D. Faddeev, "Integrable models in 1 + 1-dimensional quantum field theory," Preprint S. Ph. T. 82/76, CEN Saclay (1982).
[22]
I. V. Cherednik, "Elliptic curves and matrix soliton differential equations," in: Algebra, Geometry, Topology [in Russian], Vol. 22, VINITI Akad. Nauk SSSR, Moscow (1984), pp. 205–265.
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Published
Jul 01, 1985
Vol/Issue
19(3)
Pages
193-206
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I. V. Cherednik (1985). Functional realizations of basis representations of factoring Lie groups and algebras. Functional Analysis and Its Applications, 19(3), 193-206. https://doi.org/10.1007/bf01076619