Finite type modules and Bethe Ansatz for quantum toroidal gl(1)

Understand

We study highest weight representations of the Borel subalgebra of the quantum toroidal gl(1) algebra with finite-dimensional weight spaces.

• In particular, we develop the q-character theory for such modules.
• We introduce and study the subcategory of `finite type' modules.
• By definition, a module over the Borel subalgebra is finite type if the Cartan like current \psi^+(z) has a finite number of eigenvalues, even though the module itself can be infinite dimensional.