Geometric construction of crystal bases

DOI10.1215/S0012-7094-97-08902-XzbMath0901.17006arXivq-alg/9606009OpenAlexW2120381609MaRDI QIDQ1365159

Publication date: 1 November 1997

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9606009

zbMATH Keywords

characteristic variety perverse sheaves highest weight module singular support

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representation theory for linear algebraic groups (20G05)

Related Items

Perverse sheaves with nilpotent singular support on the stack of coherent sheaves on an elliptic curve, Preprojective algebras of $d$-representation finite species with relations, Geometric realisations of the unipotent enveloping algebra of a quiver, Affine PBW bases and affine MV polytopes, Preprojective algebras and MV polytopes, Local Euler obstructions for determinantal varieties, Geometric construction of crystal bases for quantum generalized Kac-Moody algebras, Description of crystals for generalized Kac-Moody algebras using rigged configurations, The crystal structure on the set of Mirković-Vilonen polytopes, Modules with 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A, On two geometric constructions of $U(\mathfrak {sl}_n)$ and its representations, Soergel Calculus and Schubert Calculus, On an analogue of the James conjecture, On generalized category $\mathcal O$ for a quiver variety, Classifying tilting complexes over preprojective algebras of Dynkin type, Crystal bases as tuples of integer sequences, Rigged configurations and the $\ast $-involution for generalized Kac-Moody algebras, Rigged configurations and the $\ast$-involution, A quiver variety approach to root multiplicities, Realizations of crystal $\mathcal B(\infty)$ using Young tableaux and Young walls, Rank 2 affine MV polytopes, Quantum Borcherds-Bozec algebras and their integrable representations, Reflections in a crystal, Tensor product varieties and crystals: The $ADE$ case., Rigged configuration descriptions of the crystals B(∞) and B(λ) for special linear Lie algebras, A combinatorial description of the Gindikin-Karpelevich formula in type $A$, Classical limit of quantum Borcherds-Bozec algebras, Half potential on geometric crystals and connectedness of cellular crystals, On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theory., Appearance of the Kashiwara-Saito singularity in the representation theory of $p$-adic $\mathrm{GL}(16)$, Kac-Moody groups and cluster algebras, Path realization of crystal $B(\infty )$, Affine PBW bases and MV polytopes in rank 2, Crystals from categorified quantum groups, Study of multiplicities in induced representations of $GL_n$ through a symmetric reduction, Weyl group action and semicanonical bases, A geometric realization of modified quantum algebras, The p-canonical basis for Hecke algebras, Geometric construction of highest weight crystals for quantum generalized Kac-Moody algebras, Unnamed Item, Quivers with loops and generalized crystals, Young tableaux and crystal $\mathcal B(\infty )$ for the exceptional Lie algebra types, Semicanonical bases and preprojective algebras, Tensor product varieties, perverse sheaves, and stability conditions, The transition matrix between PBW basis and semicanonical basis of $U^+(\mathfrak{s}\mathfrak{l}_n(\mathbb C))$, Categorification of integrable representations of quantum groups, Partial flag varieties and preprojective algebras., Introduction to Quiver Varieties, Homological properties of finite-type Khovanov-Lauda-Rouquier algebras., Affine Mirković-Vilonen polytopes, Erratum to: ``$B_2$-crystals: axioms, structure, models, Quiver varieties and Kac-Moody algebras, Characteristic cycles for the loop Grassmannian and nilpotent orbits., Buildings, spiders, and geometric Satake, A combinatorial categorification of the tensor product of the Kirillov-Reshetikhin crystal $B^{1,1}$ and a fundamental crystal, Crystal bases for the quantum queer superalgebra, Crystal of affine type $\widehat{A}_{\ell-1}$ and Hecke algebras at a primitive $2\ell$ th root of unity, Singularities of Schubert varieties within a right cell, Using rigged configurations to model $B(\infty)$, Rigged configurations for all symmetrizable types, Quiver Varieties and Adjoint Crystals of Level ℓ for TypeA_n⁽¹⁾, Combinatorial realizations of crystals via torus actions on quiver varieties, Extension-orthogonal components of preprojective varieties, Alcove path model for $B(\infty)$, Tensor product varieties and crystals: $GL$ case, Hecke-Clifford superalgebras, crystals of type 𝐴_{2ℓ}⁽²⁾ and modular branching rules for ̂𝑆_{𝑛}, Mirkovic-Vilonen polytopes and Khovanov-Lauda-Rouquier algebras, On intersections of orbital varieties and components of Springer fiber, Flatness for the moment map for representations of quivers., Quiver varieties and Demazure modules, On the reducibility of characteristic varieties, Hecke-Clifford superalgebras and crystals of type $D_l^{(2)}$, Geometric and combinatorial realizations of crystal graphs, Lattice structure of Weyl groups via representation theory of preprojective algebras, Quivers with relations for symmetrizable Cartan matrices. IV: Crystal graphs and semicanonical functions, Combinatorial descriptions of the crystal structure on certain PBW bases, Nakajima Monomials and Crystals for Special Linear Lie Algebras, Crystal Bases and Monomials forU_q(G₂)-Modules, On Mirković-Vilonen cycles and crystal combinatorics, Kirillov-Reshetikhin crystals, energy function and the combinatorial $R$-matrix, Reducibility of the intersections of components of a Springer fiber, Quivers with loops and perverse sheaves, Higher preprojective algebras, Koszul algebras, and superpotentials, A reducible characteristic variety in type A, Crystals, quiver varieties, and coboundary categories for Kac-Moody algebras, Imaginary vectors in the dual canonical basis of $U_q({\mathfrak n})$, Folding KLR algebras, Candidate for the crystal $B_{(-\infty)}$ for the queer Lie superalgebra, Quiver varieties and path realizations arising from adjoint crystals of type 𝐴_{𝑛}⁽¹⁾, PBW parametrizations and generalized preprojective algebras, Semicanonical bases arising from enveloping algebras, Reducible characteristic cycles of Harish-Chandra modules for U(p,q) and the Kashiwara–Saito singularity, Torsion pairs for quivers and the Weyl groups, Crystal bases and three-dimensional $\mathcal{N} = 4$ Coulomb branches, A local model for the trianguline variety and applications, Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras, Abstract crystals for quantum Borcherds–Bozec algebras, A rigged configuration model for $B(\infty)$, Equivariant multiplicities of simply-laced type flag minors, An insight into the description of the crystal structure for Mirković-Vilonen polytopes, Crystal ℬ(∞) for Quantum Affine Algebras: A Young Wall Description, NON-PERVERSE PARITY SHEAVES ON THE FLAG VARIETY

Cites Work