Virtual crystals and Nakajima monomials
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Publication:1616717
DOI10.3842/SIGMA.2018.103zbMath1400.05270arXiv1707.09638WikidataQ129187059 ScholiaQ129187059MaRDI QIDQ1616717
Ben Salisbury, Travis Scrimshaw
Publication date: 7 November 2018
Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1707.09638
Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)
Uses Software
Cites Work
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- Connecting marginally large tableaux and rigged configurations via crystals
- Zigzag strip bundles and crystals
- Zigzag strip bundles and highest weight crystals
- Crystal \(B(\lambda)\) as a subset of crystal \(B(\infty)\) expressed as tableaux for \(A_n\) type
- Zigzag strip bundle realization of \(B(\lambda_{0})\) over \(U_{q}(C_{n}^{(1)})\)
- Combinatorial descriptions of the crystal structure on certain PBW bases
- Crystal base elements of an extremal weight module fixed by a diagram automorphism
- Modified Nakajima monomials and the crystal \(B(\infty )\)
- A modification of the Anderson-Mirković conjecture for Mirković-Vilonen polytopes in types \(B\) and \(C\)
- Young tableaux and crystal \(\mathcal B(\infty)\) for finite simple Lie algebras
- Mirković-Vilonen cycles and polytopes.
- \(B_2\)-crystals: axioms, structure, models
- A definition of the crystal commutor using Kashiwara's involution
- Crystals, quiver varieties, and coboundary categories for Kac-Moody algebras
- On crystal bases of the \(q\)-analogue of universal enveloping algebras
- Perfect crystals of quantum affine Lie algebras
- Crystal bases and Young tableaux
- Polyhedral realizations of crystal bases for integrable highest weight modules
- Crystal bases and tensor product decompositions of \(U_ q(G_ 2)\)- modules
- The crystal base and Littelmann's refined Demazure character formula
- Crystal bases of modified quantized enveloping algebra
- Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
- Polyhedral realizations of crystal bases for quantized Kac-Moody algebras
- A tensor product theorem related to perfect crystals.
- Virtual crystals and Kleber's algorithm
- Tensor product multiplicities, canonical and totally positive varieties
- Virtualization map for the Littelmann path model
- Rigged configurations and the \(\ast\)-involution
- Realization of Kirillov-Reshetikhin crystals \(B^{1,s}\) for \(\widehat{\mathfrak{sl}}_n\) using Nakajima monomials
- PBW bases and marginally large tableaux in type \(D\)
- On level-zero representation of quantized affine algebras.
- Paths and root operators in representation theory
- Parametrizations of canonical bases and totally positive matrices
- Combinatorial realizations of crystals via torus actions on quiver varieties
- Crystal structure on rigged configurations and the filling map
- A rigged configuration model for \(B(\infty)\)
- On the local structure of doubly laced crystals
- The crystal structure on the set of Mirković-Vilonen polytopes
- Path realization of crystal \(B(\infty )\)
- Monomial realization of crystal bases \(B(\infty)\) for the quantum finite algebras
- Crystals and coboundary categories
- Quiver varieties and \(t\)-analogs of \(q\)-characters of quantum affine algebras
- Crystal Bases
- Crystal Base Elements of an ExtremalWeight Module Fixed by a Diagram Automorphism II: Case of Affine Lie Algebras
- Generalized Young walls and crystal bases for quantum affine algebra of type $A$
- Level 0 Monomial Crystals
- Canonical Bases Arising from Quantized Enveloping Algebras
- Existence of Kirillov–Reshetikhin crystals for nonexceptional types
- AFFINE CRYSTALS AND VERTEX MODELS
- A local characterization of simply-laced crystals
- Virtual crystals and fermionic formulas of type 𝐷_{𝑛+1}⁽²⁾, 𝐴_{2𝑛}⁽²⁾, and 𝐶_{𝑛}⁽¹⁾
- Simplicity and similarity of Kirillov-Reshetikhin crystals
- Zigzag Strip Bundles and the CrystalB(∞) for Quantum Affine Algebras
- An insight into the description of the crystal structure for Mirković-Vilonen polytopes
- Crystal structure on rigged configurations
- Zero actions and energy functions for perfect crystals
- Lakshmibai-Seshadri paths fixed by a diagram automorphism.
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