A Chevalley-Kostant presentation of basic modules for \(\widetilde {{\mathfrak {sl}}(2)}\) and the associated affine KPRV determinants at \(q=1\)

DOI10.1016/S0007-4497(00)01077-0zbMath0970.17006OpenAlexW2005024623MaRDI QIDQ5932241

Jacob Greenstein, Anthony Joseph

Publication date: 14 October 2001

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0007-4497(00)01077-0

zbMATH Keywords

KPRV determinantaffine Lie algebrashighest weightintegrable modulesquantum affine algebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (1)

On an affine quantum KPRV determinant at \(q=1\)

Cites Work

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• Clifford algebra analogue of the Hopf-Koszul-Samelson theorem, the \(\rho\)-decomposition \(C({\mathfrak g})=\text{End }V_ \rho\otimes C(P)\), and the \({\mathfrak g}\)-module structure of \(\bigwedge {\mathfrak g}\)
• Quantum affine algebras
• A completion of the quantized enveloping algebra of a Kac-Moody algebra
• Characters of bounded \(\widehat{\mathfrak{sl}}(2)\) modules.
• Representation of complex semi-simple Lie groups and Lie algebras
• On some unsolved problems in quantum group theory
• Lie Group Representations on Polynomial Rings
• On an affine quantum KPRV determinant at \(q=1\)

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