Polyhedral realizations of crystal bases for quantized Kac-Moody algebras
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Publication:1372876
DOI10.1006/aima.1997.1670zbMath0897.17014arXivq-alg/9703045OpenAlexW1963501507MaRDI QIDQ1372876
Toshiki Nakashima, Andrei V. Zelevinsky
Publication date: 4 November 1997
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/q-alg/9703045
crystal basispolyhedral realizations\(q\)-deformation of universal enveloping algebranilpotent part of Kac-Moody algebra
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Combinatorics of representations of \(U_ q (\widehat{\mathfrak sl}(n))\) at \(q=0\)
- On crystal bases of the \(q\)-analogue of universal enveloping algebras
- Perfect crystals of quantum affine Lie algebras
- A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras
- The crystal base and Littelmann's refined Demazure character formula
- Crystal bases of modified quantized enveloping algebra
- Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
- Paths and root operators in representation theory
- Canonical bases for the quantum group of type \(A_r\) and piecewise-linear combinatorics
- Parametrizations of canonical bases and totally positive matrices
- Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras
- Crystalizing the q-analogue of universal enveloping algebras
- AFFINE CRYSTALS AND VERTEX MODELS
- Introduction to quantum groups