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Identities for the Rogers dilogarithm function connected with simple Lie algebras

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Abstract

New identities are proved for the dilogarithm function connected with the Lie algebras of the series An and with classical Lie algebras of rank ⩽4.

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Literature cited

  1. L. J. Rogers, “On function sums connected with the series Σ xn/n2,” Proc. London Math. Soc.,4, 169–189 (1907).

    Google Scholar 

  2. L. Lewin, Polylogarithms and Associated Functions, North-Holland, Amsterdam (1981).

    Google Scholar 

  3. I. M. Gelfand and R. D. MacPherson, “Geometry in Grassmanians and a generalization of the dilogarithm,” Adv. Math.,44, 279–312 (1982).

    Google Scholar 

  4. G. E. Andrews, R. J. Baxter, and P. J. Forrester, “Eight-vertex SOS model and generalized Rogers-Ramanujan identities,” J. Stat. Phys.,35, 193–266 (1984).

    Google Scholar 

  5. A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, “Infinite conformal symmetry in two-dimensional quantum field theory,” Nucl. Phys.,B-241, 333–380 (1984).

    Google Scholar 

  6. V. V. Bazhanov and N. Yu. Reshetikhin, “Conformal field theory and critical RSOS models,” Serpukhov Preprint No. 27 (1987).

  7. J. J. Dupont, “The dilogarithm as a characteristic class for flat bundles,” J. Pure Appl. Math.,44, 137–164 (1987).

    Google Scholar 

  8. V. Kac and M. Wakimoto, “Modular and conformal invariance constraints in representation theory of affine algebras,” Preprint No. 13, IHES (1987).

  9. N. Bourbaki, Lie Groups and Algebras [Russian translation], Moscow (1972).

  10. A. N. Kirillov and N. Yu. Reshetikhin, “Exact solution of the Heisenberg XXZ model of spin S,” J. Sov. Math.,35, No. 4 (1986).

  11. A. N. Kirillov and N. Yu. Reshetikhin, “Representations of Yangians and multiplicities of occurrence of irreducible components of a tensor product of simple algebras,” Zap. Nauchn. Semin. Leningr. Otdel. Mat. Inst.,160, 211–222 (1987).

    Google Scholar 

  12. V. V. Bazhanov, A. N. Kirillov, and N. Yu. Reshetikhin, “Conformal field theory and critical RSOS-models, II,” Pis'ma Zh. Éks. Teor. Fiz.,46, No. 9, 500–510 (1987).

    Google Scholar 

  13. E. Cgievetsky, N. Reshetikhin, and P. Wiegmann, “The principal chiral field in two dimensions on classical Lie algebras,” Nucl. Phys.,B280, 45–96 (1987).

    Google Scholar 

  14. A. B. Zamolodchikov, “Exact solutions of two-dimensional conformal field theory and critical phenomena,” Preprint ITF-87-65R.

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Authors
  1. A. N. Kirillov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 121–133 1987.

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Kirillov, A.N. Identities for the Rogers dilogarithm function connected with simple Lie algebras. J Math Sci 47, 2450–2459 (1989). https://doi.org/10.1007/BF01840426

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  • DOI: https://doi.org/10.1007/BF01840426

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