Tensor product varieties and crystals: $GL$ case

DOI10.1090/S0002-9947-01-02899-9zbMath0990.20030arXivmath/0103026MaRDI QIDQ2759072

Anton Malkin

Publication date: 10 December 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0103026

zbMATH Keywords

Kac-Moody algebrassimple modulesLittlewood-Richardson coefficientscrystalscanonical basesirreducible componentsnilpotent orbitsSpaltenstein varietiestensor product varieties

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representation theory for linear algebraic groups (20G05) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Group actions on varieties or schemes (quotients) (14L30) Grassmannians, Schubert varieties, flag manifolds (14M15) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Varieties and morphisms (14A10)

Related Items (5)

On two geometric constructions of \(U(\mathfrak {sl}_n)\) and its representations ⋮ Comparison of quiver varieties, loop Grassmannians and nilpotent cones in type \(A\) (with an appendix by Vasily Krylov) ⋮ Tensor product varieties and crystals: The \(ADE\) case. ⋮ Springer fibers and the Delta Conjecture at \(t = 0\) ⋮ Quiver varieties and fusion products for \(\mathfrak{sl}_2\)

Cites Work

• Classes unipotentes et sous-groupes de Borel
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Crystal bases of modified quantized enveloping algebra
• Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras
• Geometric construction of crystal bases
• Tensor product varieties and crystals: The \(ADE\) case.
• Quiver varieties and tensor products
• Quiver varieties and Kac-Moody algebras
• Crystalizing the q-analogue of universal enveloping algebras
• Quivers, Perverse Sheaves, and Quantized Enveloping Algebras
• Number of Points of Varieties in Finite Fields
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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