Principal $\widehat{sl}(3)$ subspaces and quantum Toda Hamiltonian

Abstract

We study a class of representations of the Lie algebra of Laurent polynomials with values in the nilpotent subalgebra of sl(3). We derive Weyl-type (bosonic) character formulas for these representations. We establish a connection between the bosonic formulas and the Whittaker vector in the Verma module for the quantum group $U_{v}sl(3)$. We also obtain a fermionic formula for an eigenfunction of the sl(3) quantum Toda Hamiltonian.

Latex, 42 pages

References in corpus (2)

• Finite difference quantum Toda lattice via equivariant K-theory
• On a Gauss-Givental Representation of Quantum Toda Chain Wave Function

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• String Functions for Affine Lie Algebras Integrable Modules