Polyhedral realization of the highest weight crystals for generalized Kac-Moody algebras

DOI10.1090/S0002-9947-08-04446-2zbMath1159.81029OpenAlexW2080605629MaRDI QIDQ3542007

Dong-Uy Shin

Publication date: 27 November 2008

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-08-04446-2

zbMATH Keywords

crystal basishighest weight modulequantum generalized Kac-Moody algebrapolyhedral realization

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items (11)

Nakajima Monomials, Strip Bundles, and the CrystalsB(∞) OverU_q(B_∞), andU_q(C_∞), andU_q(D_∞) ⋮ Strip bundle realization of the crystals over Uq(D4(3)) ⋮ Strip Bundles and the Highest Weight Crystals Over Quantum Infinite Rank Affine Algebras ⋮ Description of crystals for generalized Kac-Moody algebras using rigged configurations ⋮ Rigged configurations and the \(\ast \)-involution for generalized Kac-Moody algebras ⋮ Zigzag strip bundles and highest weight crystals ⋮ Generalized Young walls for classical Lie algebras ⋮ Monomial Realization of the Crystals OverU_q(A_∞) and the Quantum Monster Algebra ⋮ Nakajima monomials, Young walls and Kashiwara embedding for \(U_q(A_n^{(1)})\) ⋮ Strip bundle realization of the crystals over Uq(G2(1)) ⋮ Zigzag Strip Bundles and the CrystalB(∞) for Quantum Affine Algebras

Cites Work

• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Generalized Kac-Moody algebras
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Crystal bases and Young tableaux
• Polyhedral realizations of crystal bases for integrable highest weight modules
• The crystal base and Littelmann's refined Demazure character formula
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Polyhedral realizations of crystal bases for quantized Kac-Moody algebras
• Monstrous moonshine and monstrous Lie superalgebras
• Quantum deformations of generalized Kac-Moody algebras and their modules
• Paths and root operators in representation theory
• Crystalizing the q-analogue of universal enveloping algebras
• Monstrous Moonshine
• AFFINE CRYSTALS AND VERTEX MODELS
• CRYSTAL BASES FOR QUANTUM AFFINE ALGEBRAS AND COMBINATORICS OF YOUNG WALLS
• Crystal bases for quantum generalized kac–moody algebras
• Abstract Crystals for Quantum Generalized Kac-Moody Algebras
• Polyhedral realization of crystal bases for generalized Kac-Moody algebras

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