Geometric construction of the global base of the quantum modified algebra of \(\hat{\mathfrak g}{\mathfrak l}_N\)

DOI10.1007/BF01234797zbMath0978.17007MaRDI QIDQ5927628

Olivier Schiffmann, Eric Vasserot

Publication date: 7 February 2002

Published in: Transformation Groups (Search for Journal in Brave)

zbMATH Keywords

affine flag varietycanonical baseconjecture of Lusztigintersection cohomology sheavesquantum algebra of \({\mathfrak gl}_n\)

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Special varieties (14M99)

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Monomial bases for $q$-Schur algebras ⋮ Generalized \(q\)-Schur algebras and quantum Frobenius ⋮ Positivity VS Negativity of Canonical Bases ⋮ Comparison of canonical bases for Schur and universal enveloping algebras ⋮ Affine flag varieties and quantum symmetric pairs ⋮ A geometric realization of modified quantum algebras ⋮ The comultiplication of modified quantum affine 𝔰𝔩n ⋮ Affine flag varieties and quantum symmetric pairs. II: Multiplication formula ⋮ A geometric realization of quantum groups of type \(\mathbf D\) ⋮ Geometric Schur duality of classical type ⋮ Geometric Schur duality of classical type, II ⋮ Affine Hecke algebras and quantum symmetric pairs

Cites Work

• A geometric setting for the quantum deformation of \(\mathrm{GL}_n\)
• Double-loop algebras and the Fock space
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Affine quantum groups and equivariant \(K\)-theory
• Crystal bases of modified quantized enveloping algebra
• On the decomposition matrices of the quantized Schur algebra
• Crystal base for the basic representation of \(U_ q({\mathfrak sl}^\wedge (n))\)
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