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Universal exponential solution of the Yang-Baxter equation

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Abstract

Exponential solutions of the Yang-Baxter equation give rise to generalized Schubert polynomials and corresponding symmetric functions. We provide several descriptions of the local stationary algebra defined by this equation. This allows us to construct various exponential solutions of the YBE. The B n and G 2 cases are also treated.

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References

  1. Bergeron, N.: The structure of the universal exponential solution of the Yang-Baxter equation, Math. Res. Lett. 1 (1994), 99–105.

    Google Scholar 

  2. Fomin, S.: Duality of graded graphs, J. Algebraic Combin. 3 (1994), 357–404.

    Google Scholar 

  3. Fomin, S. and Kirillov, A. N.: The Yang-Baxter equation, symmetric functions, and Schubert polynomials, Proc. 5th Internat. Conf. on Formal Power Series and Algebraic Combinatorics, Firenze, 1993, 215–229; to appear in Discrete Math.

  4. Fomin, S. and Kirillov, A. N.: Grothendieck polynomials and the Yang-Baxter equation, Proc. 6th Internat. Conf. Formal Power Series and Algebraic Combinatorics, DIMACS, 1994, pp. 183–190.

  5. Fomin, S. and Kirillov, A. N.: Combinatorial B n-analogues of Schubert polynomials, to appear in Trans. Amer. Math. Soc.

  6. Fomin, S. and Stanley, R. P.: Schubert polynomials and the nilCoxeter algebra, Adv. in Math. 103 (1994), 196–207.

    Google Scholar 

  7. Lascoux, A.: Polynômes de Schubert. Une approche historique, in: P.Leroux and C.Reutenauer (eds), Séries formelles et combinatoire algébrique, Montréal, LACIM, UQAM, 1992, pp. 283–296.

    Google Scholar 

  8. Lascoux, A. and Schützenberger, M. P.: Décompositions dans l'algèbre des differences divisées, Preprint, 1989.

  9. Macdonald, I.: Notes on Schubert polynomials, Laboratoire de combinatoire et d'informatique mathématique (LACIM), Université du Québec à Montréal, Montréal, 1991.

    Google Scholar 

  10. Rogawski, J. D.: On modules over the Hecke algebras of a p-adic group, Invent. Math. 79 (1985), 443.

    Google Scholar 

  11. Stanley, R. P.: Differential posets, J. Amer. Math. Soc. 1 (1988), 919–961.

    Google Scholar 

  12. Verma, D.: Structure of certain induced representations of complex semisimple Lie algebras, Bull. Amer. Math. Soc. 74 (1968), 160–166.

    Google Scholar 

  13. Vershik, A. M.: Local stationary algebras, Amer. Math. Soc. Transl. (2) 148 (1991), 1–13.

    Google Scholar 

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Partially supported by the NSF (DMS-9400914).

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Fomin, S., Kirillov, A.N. Universal exponential solution of the Yang-Baxter equation. Letters in Mathematical Physics 37, 273–284 (1996). https://doi.org/10.1007/BF00343191

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  • DOI: https://doi.org/10.1007/BF00343191

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