Introduction to Quantum Groups and Crystal Bases

By Jin Hong, Seok-Jin Kang. 2002

602 citations recorded by the source corpus.

Subfields: Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/8f32b90157e1cb4e2c5e64075b31f49761155bfe

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In Physical and Theoretical Chemistry

1. S. Kolb
2. Daniel Bump
3. Ben Brubaker
4. S. Friedberg
5. Masaki Kashiwara
6. Kiumars Kaveh
7. Seok-Jin Kang

Citations in the corpus

• Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (2011, methodology): “The tensor product operation on crystals is described in Kashiwara and Nakashima [26], or in Hong and Kang [23].”
• Quantum symmetric Kac–Moody pairs (2012, methodology): “ntum symmetric pair coideal subalgebras as qtends to 1. This is done using non-restricted specialization as QUANTUM SYMMETRIC KAC-MOODY PAIRS 41 outlined in [CK90, 1.5]. We follow the presentation in [HK96]. All through this section we abbreviate k= K(q). 10.1. Specialization of θq(X,τ). We recall s”
• Crystal bases and Newton–Okounkov bodies (2011, background): “arametrization 13 3.1. Perfect bases and crystal bases. In this section we recall some background material about the crystal bases and crystal graphs of representations. Some references are [Kash95], [HoKa02], [BeKa07] and [KKKS14]. Let V be a finite dimensional G-module. Let α be a simple root with ”
• Mirković–Vilonen polytopes and Khovanov–Lauda–Rouquier algebras (2012, background): “object arising from the theory of crystal bases for the corresponding quantum group (see e.g. [Kas95]). This section contains a brief explanation of the results we need, roughly following [Kas95] and [HK02], to which we refer the reader for details. We start with a combinatorial notion of crystal th”
• Continuous crystal and Duistermaat-Heckman measure for Coxeter groups (2008, background): “[16], [18], [19], [22] for an introduction to this theory.”
• Kirillov–Reshetikhin crystals for nonexceptional types (2008, unknown): “As a {1, 2, . . . , n − 1}-crystal (4.1) Br,s ∼= B(sΛr) which as a set are all semi-standard Young tableaux of rectangular shape (sr) over the alphabet 1 ≺ 2 ≺ · · · ≺ n.”
• Elements of Vasiliev theory (2014, background): “The general rules, when both factors are generic Young diagrams, are quite complicated and can be found, for example, in [126].”
• Crystals from categorified quantum groups (2009, background): “For a good introduction to crystal graphs see [28] or [21].”
• Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux (2011, methodology): “This algorithm is an analogue of the rule for decomposing the tensor product of crystal bases of Uq(gl(n))-modules in [16] (see also [7]), which coincides with the classical Littlewood-Richardson rule.”