Symmetric crystals and affine Hecke algebras of type \(B\).

DOI10.3792/pjaa.82.131zbMath1130.20008arXivmath/0608079OpenAlexW1617476666MaRDI QIDQ883667

Masaki Kashiwara, Naoya Enomoto

Publication date: 6 June 2007

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

Full work available at URL: https://arxiv.org/abs/math/0608079

zbMATH Keywords

Lie algebrasirreducible representationsdecomposition matricesaffine Hecke algebrascrystal basesLascoux-Leclerc-Thibon conjectureLLT conjecture

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08)

Related Items

SVV algebras, On Morita equivalences between KLR algebras and VV algebras, Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras, Crystals from categorified quantum groups, Convolution products and R-matrices for type B quiver Hecke algebras, Crystals and affine Hecke algebras of type D, Symmetric crystals for \(\mathfrak{gl}_{\infty}\), Affine Hecke algebras and generalizations of quiver Hecke algebras of type B, Morita equivalences for cyclotomic Hecke algebras of type B and D

Cites Work

• On representations of affine Hecke algebras of type \(B\).
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• On the decomposition numbers of the Hecke algebra of \(G(m,1,n)\)
• Instantons and affine algebras. I: The Hilbert scheme and vertex operators
• Hecke algebras at roots of unity and crystal bases of quantum affine algebras
• Canonical Bases Arising from Quantized Enveloping Algebras