Polyhedral realizations for \(B(\infty)\) and extended Young diagrams, Young walls of type \(\mathrm{A}^{(1)}_{n-1}\), \(\mathrm{C}^{(1)}_{n-1}\), \(\mathrm{A}^{(2)}_{2n-2}\), \(\mathrm{D}^{(2)}_n\)

DOI10.1007/s10468-022-10172-zzbMath1527.17010arXiv2110.14140OpenAlexW4306846762MaRDI QIDQ6070292

Yuki Kanakubo

Publication date: 20 November 2023

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.14140

zbMATH Keywords

combinatoricsquantum groupscrystalspolyhedral realizations

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups (quantized function algebras) and their representations (20G42)

Related Items (1)

Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type \(\mathrm{A}^{(1)}_{n-1}, \mathrm{C}^{(1)}_{n-1}, \mathrm{A}^{(2)}_{2n-2}, \mathrm{D}^{(2)}_n\)

Cites Work

• Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
• Cones, crystals, and patterns
• Combinatorics of representations of \(U_ q (\widehat{\mathfrak sl}(n))\) at \(q=0\)
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Fock space representations of the quantized universal enveloping algebras \(U_ q(C^{(1)}_ l)\), \(U_ q(A^{(2)}_{2l})\), and \(U_ q(D^{(2)}_{l+1})\)
• 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
• Tensor product multiplicities, canonical and totally positive varieties
• Fock space representations and crystal bases for \(C_{n}^{(1)}\)
• Combinatorics of canonical bases revisited: type A
• Crystal bases of the Fock space representations and string functions
• Monomial realization of crystal bases \(B(\infty)\) for the quantum finite algebras
• Crystalizing the q-analogue of universal enveloping algebras
• Crystal base for the basic representation of \(U_ q({\mathfrak sl}^\wedge (n))\)
• Polyhedral realizations of crystal bases for quantum algebras of finite types
• Canonical Bases Arising from Quantized Enveloping Algebras
• CRYSTAL BASES FOR QUANTUM AFFINE ALGEBRAS AND COMBINATORICS OF YOUNG WALLS
• Adapted sequence for polyhedral realization of crystal bases
• Polyhedral realizations of crystal bases for quantum algebras of classical affine types

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