Heisenberg realization for U_q(sln) on the flag manifold

Abstract

We give the Heisenberg realization for the quantum algebra $U_q(s{l}_n)$, which is written by the $q$-difference operator on the flag manifold. We construct it from the action of $U_q(s{l}_n)$ on the $q$-symmetric algebra $A_q(Ma{t}_n)$ by the Borel-Weil like approach. Our realization is applicable to the construction of the free field realization for the $U_q(\widehat{s{l}_n})$ [AOS].

arXiv comment10 pages, YITP/K-1016, plain TEX (some mistakes corrected and a reference added)

References in corpus (3)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Diagonalization of the XXZ Hamiltonian by Vertex Operators
• Free Field Representation of Quantum Affine Algebra U_q(\hat{sl}_2)

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• Free Field Realization of Quantum Affine Superalgebra $U_q(\widehat{sl}(N|1))$
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