Dual canonical bases, quantum shuffles and \(q\)-characters
From MaRDI portal
Publication:1434210
DOI10.1007/s00209-003-0609-9zbMath1052.17008arXivmath/0209133OpenAlexW2046115991MaRDI QIDQ1434210
Publication date: 1 July 2004
Published in: Mathematische Zeitschrift (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0209133
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08)
Related Items
Affine PBW bases and affine MV polytopes ⋮ Imaginary Schur-Weyl duality ⋮ Representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras ⋮ Using Catalan words and a \(q\)-shuffle algebra to describe the Beck PBW basis for the positive part of \(U_q( \widehat{\mathfrak{sl}}_2)\) ⋮ The existence of greedy bases in rank 2 quantum cluster algebras ⋮ PBW bases for a class of braided Hopf algebras. ⋮ Feigin's map revisited ⋮ On the cohomology of quiver Grassmannians for acyclic quivers ⋮ Canonical bases for the quantum supergroup U(𝔤𝔩3|1) ⋮ An infinite-dimensional \(\square_q\)-module obtained from the \(q\)-shuffle algebra for affine \(\mathfrak{sl}_2\) ⋮ Dominance order and monoidal categorification of cluster algebras ⋮ Quantizations of Kac-Moody algebras. ⋮ Newton-Okounkov bodies for categories of modules over quiver Hecke algebras ⋮ Representations of orientifold Khovanov-Lauda-Rouquier algebras and the Enomoto-Kashiwara algebra ⋮ Crystal base of the negative half of the quantum superalgebra \(U_q( \mathfrak{gl}(m | n))\) ⋮ Nakajima's quiver varieties and triangular bases of rank-2 cluster algebras ⋮ A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems. ⋮ Using a q-shuffle algebra to describe the basic module V(Λ_0) for the quantized enveloping algebra Uq(sl^2) ⋮ Rational Cherednik algebras of \(G (\ell, p, n)\) from the Coulomb perspective ⋮ Elementary construction of Lusztig’s canonical basis ⋮ Shuffle algebras for quivers and wheel conditions ⋮ Convex PBW-type Lyndon bases and restricted two-parameter quantum group of type \(F_4\) ⋮ Canonical bases for the quantum supergroups \(\mathbf U(\mathfrak{gl}_{m|n})\) ⋮ Quantum loop groups and shuffle algebras via Lyndon words ⋮ Quantum unipotent subgroup and dual canonical basis ⋮ Enveloping algebras and geometric representation theory. Abstracts from the workshop held October 31 -- November 6, 2021 (hybrid meeting) ⋮ Dual canonical bases for the quantum special linear group and invariant subalgebras ⋮ Kac-Moody groups and cluster algebras ⋮ Degenerate affine Hecke-Clifford algebras and type \(Q\) Lie superalgebras. ⋮ Representations of quiver Hecke algebras via Lyndon bases. ⋮ Crystals from categorified quantum groups ⋮ PBW-bases of coideal subalgebras and a freeness theorem ⋮ Semicanonical bases and preprojective algebras ⋮ Hopf algebras and Markov chains: two examples and a theory ⋮ Homological properties of finite-type Khovanov-Lauda-Rouquier algebras. ⋮ Cuspidal systems for affine Khovanov-Lauda-Rouquier algebras. ⋮ Using Catalan words and a \(q\)-shuffle algebra to describe a PBW basis for the positive part of \(U_q(\widehat{\mathfrak{sl}}_2)\) ⋮ Crystals and affine Hecke algebras of type D ⋮ Quantum invariants for decomposition problems in type \(A\) rings of representations ⋮ QUANTISATION SPACES OF CLUSTER ALGEBRAS ⋮ A diagrammatic approach to categorification of quantum groups I ⋮ Cohomological Hall algebras and affine quantum groups ⋮ Representations of Khovanov-Lauda-Rouquier algebras and combinatorics of Lyndon words. ⋮ Representation theory of symmetric groups and related Hecke algebras ⋮ Combinatorial descriptions of the crystal structure on certain PBW bases ⋮ Quantum groups via cyclic quiver varieties I ⋮ Completely splittable representations of affine Hecke-Clifford algebras. ⋮ The alternating PBW basis for the positive part of Uq(sl^2) ⋮ Graded decomposition numbers for cyclotomic Hecke algebras. ⋮ Equivariant multiplicities via representations of quantum affine algebras ⋮ Equivariant multiplicities of simply-laced type flag minors