Principal sl(3) subspaces and quantum Toda Hamiltonian

2007/07/11 by Boris Feigin, Evgeny Feigin, Feigin, B. +7 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.0707.1635

openalex publication_date 2007/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On a Gauss-Givental Representation of Quantum Toda Chain Wave Function

Cited by

• On a property of branching coefficients for affine Lie algebras

Related

• Resolutions and a Weyl Character formula for prime representations of quantum affine sl_n+1
• Gelfand-Zetlin basis, Whittaker vectors and a bosonic formula for the \sln principal subspace
• Jet Schemes, Quantum Dilogarithm and Feigin-Stoyanovsky's Principal Subspaces
• On explicit realization of algebra of complex powers of generators of U_q(\mathfraksl(3))
• Quantum Lie algebras of type A_n