  We solve the recently proposed T- and Y-systems (Hirota equation) for the
exact spectrum of AdS/CFT in the strong coupling scaling limit for an arbitrary
quasiclassical string state. The corresponding T-functions appear to be
super-characters of the SU(2,2|4) group in unitary representations with a
highest weight, with the classical AdS5xS5 superstring monodromy matrix as the
group element. We propose a concise first Weyl-type formula for these
characters and show that they correctly reproduce the results of quasiclassical
one-loop quantization in all sectors of the superstring, under some natural
assumptions. We also speculate about possible relation between the T-functions
and the quantum monodromy matrix.
