@article{2c121e65cf344508b423c5ab5993cce9,

title = "Fermionic formulas for eigenfunctions of the difference toda hamiltonian",

abstract = "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.",

keywords = "Difference Toda Hamiltonian, Fermionic formulas, Quantum groups",

author = "B. Feigin and E. Feigin and M. Jimbo and T. Miwa and E. Mukhin",

note = "Funding Information: Research of BF is partially supported by RFBR grants 08-01-00720-a, NSh-3472.2008.2 and 07-01-92214-CNRSL-a. Research of EF is supported by the RFBR Grants 06-01-00037, 07-02-00799 and NSh-3472.2008.2, by Pierre Deligne fund based on his 2004 Balzan prize in mathematics, by Euler foundation and by Alexander von Humboldt Fellowship. Research of MJ is supported by the Grant-in-Aid for Scientific Research B-20340027 and B-20340011. Research of TM is supported by the Grant-in-Aid for Scientific Research B-17340038. Research of EM is supported by NSF grant DMS-0601005. The present work has been carried out during the visits of BF, EF and EM to Kyoto University. They wish to thank the University for hospitality. This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.",

year = "2009",

month = jun,

doi = "10.1007/s11005-009-0300-0",

language = "אנגלית",

volume = "88",

pages = "39--77",

journal = "Letters in Mathematical Physics",

issn = "0377-9017",

publisher = "Springer Netherlands",

number = "1-3",

}