Translator Disclaimer
Open Access
VOL. 54 | 2009 Principal $\widehat{\mathfrak{sl}_3}$ subspaces and quantum Toda Hamiltonian
Boris Feigin, Evgeny Feigin, Michio Jimbo, Tetsuji Miwa, Evgeny Mukhin

Editor(s) Tetsuji Miwa, Atsushi Matsuo, Toshiki Nakashima, Yoshihisa Saito

Abstract

We study a class of representations of the Lie algebra $\mathfrak{n} \otimes \mathbb{C} [t, t^{-1}]$, where $\mathfrak{n}$ is a nilpotent subalgebra of $\mathfrak{sl}_3$. 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 $U_v (\mathfrak{sl}_3)$. We also obtain a fermionic formula for an eigenfunction of the $\mathfrak{sl}_3$ quantum Toda Hamiltonian.

Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1206.17012
MathSciNet: MR2499555

Digital Object Identifier: 10.2969/aspm/05410109

Subjects:
Primary: 17B37 , 17B65

Keywords: affine Lie algebras , fermionic formulas , quantum groups , Toda Hamiltonian

Rights: Copyright © 2009 Mathematical Society of Japan

PROCEEDINGS ARTICLE
58 PAGES


SHARE
Back to Top