Fermionic Formulas for Eigenfunctions of the Difference Toda Hamiltonian

  • B. Feigin
  • E. Feigin
  • M. Jimbo
  • T. Miwa
  • E. Mukhin


We use the Whittaker vectors and the Drinfeld Casimir element to show that eigenfunctions of the difference Toda Hamiltonian can be expressed via fermionic formulas. Motivated by the combinatorics of the fermionic formulas we use the representation theory of the quantum groups to prove a number of identities for the coefficients of the eigenfunctions.

Mathematics Subject Classification (2000)

37K10 17B37 


difference Toda Hamiltonian quantum groups fermionic formulas 


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Copyright information

© Springer 2009

Authors and Affiliations

  • B. Feigin
    • 1
    • 2
    • 3
  • E. Feigin
    • 4
    • 5
  • M. Jimbo
    • 6
    • 7
  • T. Miwa
    • 8
  • E. Mukhin
    • 9
  1. 1.Landau Institute for Theoretical PhysicsChernogolovkaRussia
  2. 2.Higher School of EconomicsMoscowRussia
  3. 3.Independent University of MoscowMoscowRussia
  4. 4.Tamm Theory DivisionLebedev Physics InstituteMoscowRussia
  5. 5.Mathematical InstituteUniversity of CologneCologneGermany
  6. 6.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan
  7. 7.Institute for the Physics and Mathematics of the UniverseKashiwa, ChibaJapan
  8. 8.Department of Mathematics, Graduate School of ScienceKyoto UniversityKyotoJapan
  9. 9.Department of MathematicsIndiana University-Purdue University-IndianapolisIndianapolisUSA

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