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Orbital theory for affine Lie algebras

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References

  1. Albeverio, S., Høegh-Krøhn, R.: The energy representytion of Sobolev-Lie groups. Compositio Math.36, 37–52 (1978)

    Google Scholar 

  2. Dollard, J.D., Friedman, C.N.: Product integration. Encyplopedia of Mathematics and its applications, vol. 16, London-Amsterdam-Don Mills, Ontario-Sydney-Tokyo: Addison-Wesley 1979

    Google Scholar 

  3. Elworthy, K.D., Truman, A.: Classical mechanics, the diffusion (heat) equation and the Schrodinger equation on a Riemannian manifold. J. Math. Phys.22, 2144–2166 (1981)

    Google Scholar 

  4. Fegan, H.G.: The heat equation on a compact Lie group. Trans. Amer. Math. Soc.246, 339–357 (1978)

    Google Scholar 

  5. Frenkel, I.B., Kač, V.G.: Basic representations of affine Lie algebras and dual resonance models. Invent. Math.62, 23–66 (1980)

    Google Scholar 

  6. Frenkel, I.B.: Two constructions of affine Lie algebra representations and boson-femion correspondence in quantum field theory. J. Functional Analysis44, 259–327 (1981)

    Google Scholar 

  7. Garland, H.: Dedekind's η-function and the cohomology of infinite dimensional Lie algebras. Proc. Nat. Acad. Sci. U.S.A.72, 2493–2495 (1975)

    Google Scholar 

  8. Garland, H.: The arithmetic theory of loop algebras. J. Algebra53, 480–551 (1978)

    Google Scholar 

  9. Garland, H.: The arithmetic theory of loop groups. Publ. Math. I.H.E.S.52, 181–312 (1980)

    Google Scholar 

  10. Garland, H., Lepowsky, J.: Lie algebra homology and the Macdonald-Kac formulas. Invent. Math.34, 37–76 (1976)

    Google Scholar 

  11. Gelfand, I.M., Graev, M.I., Veršik, A.M.: Representations of the group of smooth mappings of a manifoldX into a compact Lie group. Compositio Math.35, 299–334 (1977)

    Google Scholar 

  12. Gelfand, I.M., Yaglom, A.M.: Integration in functional spaces and its applications in quantum physics. J. Mathematical Phys.1, 48–69 (1960)

    Google Scholar 

  13. Harish-Chandra: Differential operators on a semisimple Lie algebra. Amer. J. Math.79, 87–120 (1957)

    Google Scholar 

  14. Hartman, P.: Ordinary differential equations. New York: John Wiley & Sons 1964

    Google Scholar 

  15. Ito, K.: Brownian motion in a Lie group. Proc. Japan Acad.26, 4–10 (1950)

    Google Scholar 

  16. Kač, V.G.: Simple irreducible graded Lie algebras of finite growth. Math. USSR-Izv.2, 1271–1311 (1968)

    Google Scholar 

  17. Kač, V.G.: Infinite-dimensional Lie algebras, Dedekind's η-function, classical Möbius function and the very strange formula, Advances in Math.30, 85–136 (1978)

    Google Scholar 

  18. Kirillov, A.A.: Elements of the theory of representations. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  19. Kirillov, A.A.: The characters of unitary representations of Lie groups. Funkt. analys i ego prilozh.2, 40–55 (1968). English translation: Funct. Anal. Appl. 2, 133–146 (1968)

    Google Scholar 

  20. Kostant, B.: On Macdonald's η-function formula, the Laplacian and generalized exponents. Advances in Math.20, 179–212 (1976)

    Google Scholar 

  21. Kuo, H.-H.: Gaussian Measures in Banach Spaces. Lecture Notes in Mathematics, vol.463. Berlin-Heidelberg-New York: Springer 1975

    Google Scholar 

  22. Loojenga, E.: Root systems and elliptic curves. Invent. Math.38, 17–32 (1976)

    Google Scholar 

  23. Macdonald, I.G.: Affine root systems and Dedekin's η-function. Invent. Math.15, 91–143 (1972)

    Google Scholar 

  24. McKean, H.P.: Stochastic integrals. New York: Academic Press 1969

    Google Scholar 

  25. Moody, R.V.: A new class of Lie algebras. J. Algebra10, 211–230 (1968)

    Google Scholar 

  26. Rossmann, W.: Kirillov's character formula for reductive Lie groups. Invent. Math.48, 207–220 (1978)

    Google Scholar 

  27. Truman, A.: The Feynman maps and the Wiener integral. J. Mathematical Phys.19, 1742–1750 (1978)

    Google Scholar 

  28. Varadarajan, V.S.: Harmonic Analysis on Real Reductive Lie Groups. Lecture Notes in Mathematics, vol. 576. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  29. Vergne, M.: On Rossmann's character formula for discrete series. Invent. Math.54, 11–14 (1979)

    Google Scholar 

  30. Yosida, K.: Functional analysis. Berlin-Heidelberg-New York: Springer 1965

    Google Scholar 

  31. Nomizu, K.: Lie groups and differential geometry. Mathematical Society of Japan: Tokyo, 1956

    Google Scholar 

  32. Lang, S.: Elliptic functions. London-Amsterdam-Don Mills, Ontario-Sydney-Tokyo: Addison-Wesley 1973

    Google Scholar 

  33. Montgomery, D., Zippin, L.: Topological transformation groups. New York: Interscience 1966

    Google Scholar 

  34. Krein, M.G.: On some new Banach algebras and Wiener-Lévy type theorems for Fourier series and integrals. Amer. Math. Soc. Transl.93, 177–199 (1970)

    Google Scholar 

  35. Strichartz, R.S.: Multipliers on fractional Sobolev spaces. J. Math. Mech.16, 1031–1060 (1967)

    Google Scholar 

  36. Gelfand, I.M.: Generalized functions, Vol. 4, New York: Academic Press, 1964

    Google Scholar 

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Frenkel, I.B. Orbital theory for affine Lie algebras. Invent Math 77, 301–352 (1984). https://doi.org/10.1007/BF01388449

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