Crystal bases for $U_{q}(\Gamma (\sigma _{1},\sigma _{2},\sigma _{3}))$

DOI10.1090/S0002-9947-01-02842-2zbMath0999.17027MaRDI QIDQ2716161

Yi Ming Zou

Publication date: 6 June 2001

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

zbMATH Keywords

Lie superalgebracrystal basesinfinite dimensional representation\(q\)-deformation of the universal enveloping algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (2)

Dual canonical bases for the quantum general linear supergroup ⋮ The first fundamental theorem of invariant theory for the orthosymplectic supergroup

Cites Work

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• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Crystal bases for \(U_q(osp (1,2r))\)
• The crystal base and Littelmann's refined Demazure character formula
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Finite dimensional representations of \(\Gamma(\sigma_ 1,\sigma_ 2,\sigma_ 3)\)
• Crystalizing the q-analogue of universal enveloping algebras
• Crystal bases for $U_q(sl(2,1))$
• Deformation of the Universal Enveloping Algebra of Γ (σ1, σ2, σ3)
• Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$
• Lie superalgebras

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