A proof of the second Rogers-Ramanujan identity via Kleshchev multipartitions

DOI10.3792/pjaa.99.005zbMath1528.11111arXiv2205.06038OpenAlexW4323043112MaRDI QIDQ6097361

Shunsuke Tsuchioka

Publication date: 5 June 2023

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.06038

zbMATH Keywords

Hecke algebrasquantum groupsRogers-Ramanujan identitiesinteger partitionsKashiwara crystals

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (1)

PBW bases of irreducible Ising modules

Cites Work

• A plactic algebra for semisimple Lie algebras
• On the connection between Young walls and Littelmann paths
• The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
• Lie algebraic approaches to classical partition identities
• \texttt{qMultiSum} -- a package for proving \(q\)-hypergeometric multiple summation identities
• Kleshchev multipartitions and extended Young diagrams
• On the tensor product of two basic representations of \(U_v(\hat s l_e)\)
• Crystal base for the basic representation of \(U_ q({\mathfrak sl}^\wedge (n))\)
• Rogers-Ramanujan identities and the Robinson-Schensted-Knuth correspondence
• On a Rogers-Ramanujan type identity from crystal base theory
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