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Kac-Moody Groups and Integrability of Soliton Equations
Boris Feigin, Edward Frenkel
A new approach to integrability of affine Toda field theories and closely related to them KdV hierarchies is proposed. The flows of a hierarchy are explicitly identified with infin…
Integrals of Motion and Quantum Groups
Boris Feigin, Edward Frenkel
A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohom…
Crystal bases, dilogarithm identities and torsion in algebraic K-groups
Edward Frenkel, Andras Szenes
We give a new interpretation and proof of the dilogarithm identities, associated to the affine Kac-Moody algebra sl(2)^, using the path description of the corresponding crystal bas…
Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities
Boris Feigin, Edward Frenkel
We prove that the dimensions of coinvariants of certain nilpotent subalgebras of the Virasoro algebra do not change under deformation in the case of irreducible representations of…