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Lakshmibai–Seshadri paths of level-zero shape and one-dimensional sums associated to level-zero fundamental representations

Part of: Lie algebras and Lie superalgebras Equilibrium statistical mechanics Groups and algebras in quantum theory

Published online by Cambridge University Press:  01 November 2008

Satoshi Naito  and
Daisuke Sagaki
Satoshi Naito
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan (email: naito@math.tsukuba.ac.jp)
Daisuke Sagaki
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan (email: sagaki@math.tsukuba.ac.jp)
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Abstract

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We give an interpretation of the energy function and classically restricted one-dimensional sums associated to tensor products of level-zero fundamental representations of quantum affine algebras in terms of Lakshmibai–Seshadri paths of level-zero shape.

Keywords

crystal basesLakshmibai–Seshadri pathslevel-zero representationsKirillov–Reshetikhin modulesquantum affine algebras

MSC classification

Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations 81R50: Quantum groups and related algebraic methods 82B23: Exactly solvable models; Bethe ansatz
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 6 , November 2008 , pp. 1525 - 1556
Copyright
Copyright © Foundation Compositio Mathematica 2008