Parametrizations of canonical bases and totally positive matrices
From MaRDI portal
Publication:1924006
DOI10.1006/aima.1996.0057zbMath0966.17011OpenAlexW2002168116WikidataQ105615329 ScholiaQ105615329MaRDI QIDQ1924006
Arkady Berenstein, Andrei V. Zelevinsky, Fomin, Sergey
Publication date: 17 November 1996
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/ec4f738fcff3016e12a86fd76d9f79729cae0282
Weyl groupquantum grouptotal positivitycanonical basisquivers of type \(A\)Chamber AnsatzFekete criterionLusztig varietyLusztig's transition maps
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
TOROIDAL q-OPERS, The quantum group U̇ and flag manifolds over the semifield Z, Quasi-homomorphisms of quantum cluster algebras, Elementary construction of Lusztig’s canonical basis, Stratification of spaces of locally convex curves by itineraries, A classification of peak-pit maximal Condorcet domains, Wilson lines and their Laurent positivity, Totally positive kernels, Pólya frequency functions, and their transforms, Symmetric Toda, gradient flows, and tridiagonalization, Characterizing total positivity: Single vector tests via linear complementarity, sign non‐reversal and variation diminution, Positive Populations, Tetrahedron equation and quantum cluster algebras, Twist automorphisms and Poisson structures, Parity duality for the amplituhedron, Sign non‐reversal property for totally non‐negative and totally positive matrices, and testing total positivity of their interval hull, Geometric lifting of the canonical basis and semitoric degenerations of Richardson varieties, Total positivity: tests and parametrizations., The Lusztig cones of a quantized enveloping algebra of type A., Subtraction-free complexity, cluster transformations, and spanning trees, Moment curves and cyclic symmetry for positive Grassmannians, Total positivity of Toeplitz matrices of recursive hypersequences, Total Positivity in Reductive Groups, II, Cluster theory of the coherent Satake category, Grassmann convexity and multiplicative Sturm theory, revisited, A qd-type method for computing generalized singular values of BF matrix pairs with sign regularity to high relative accuracy, Total positivity, Grassmannian and modified Bessel functions, Auslander-Reiten quiver of type A and generalized quantum affine Schur-Weyl duality, Electrical varieties as vertex integrable statistical models, The number of connected components in double Bruhat cells for nonsimply-laced groups, Coordinate rings and birational charts, Virtual crystals and Nakajima monomials, A super-class walk on upper-triangular matrices, Totally positive Toeplitz matrices and quantum cohomology of partial flag varieties, Chambers of wiring diagrams, Total positivity, Schubert positivity, and geometric Satake, On Landau-Ginzburg models for quadrics and flat sections of Dubrovin connections, Generalized totally nonnegative matrices, Twists of Plücker coordinates as dimer partition functions, The center of the affine nilTemperley-Lieb algebra, Positroid cluster structures from relabeled plabic graphs, Quantum twist maps and dual canonical bases, Preservers of totally positive kernels and Pólya frequency functions, Polyhedral realizations of crystal bases for quantized Kac-Moody algebras, On maximal weakly separated set-systems, A crystal embedding into Lusztig data of type \(A\), Polyhedral parametrizations of canonical bases \& cluster duality, The Archimedean limit of random sorting networks, Discrete solitons in infinite reduced words, The Chamber Ansatz for quantum unipotent cells, Combinatorics of canonical bases revisited: string data in type \textsf{A}, A path-counting analysis of phase shifts in box-ball systems, Decorations on geometric crystals and monomial realizations of crystal bases for classical groups, Symplectic groupoids for cluster manifolds, A cluster realization of \(U_q(\mathfrak {sl}_{\mathfrak {n}})\) from quantum character varieties, Some algebraic structures in KPZ universality, Yang-Baxter maps and integrable dynamics, Poisson geometry of directed networks in an annulus, Lusztig factorization dynamics of the full Kostant-Toda lattices, Finiteness of rank for Grassmann convexity, Combinatorics of X-variables in finite type cluster algebras, Complexity of tropical Schur polynomials, Crystals and total positivity on orientable surfaces, Condorcet domains of tiling type, Multiplicative principal-minor inequalities for totally nonnegative matrices, Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties, Monotonicity of strata in the stratification of the cone of totally positive matrices, Mini-workshop: Scattering amplitudes, cluster algebras, and positive geometries. Abstracts from the mini-workshop held December 5--11, 2021 (hybrid meeting), Cluster algebras in algebraic Lie theory, Total positivity for loop groups. II: Chevalley generators, Total positivity in loop groups. I: Whirls and curls, Geometrical lifting of the canonical base and Schützenberger involution, Cluster ensembles and Kac-Moody groups, Generalized Bäcklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective, Representation theory over tropical semifield and Langlands duality, Canonical basis linearity regions arising from quiver representations., Geometric RSK and the Toda lattice, Factorizations in Schubert cells, On the cluster nature and quantization of geometric \(R\)-matrices, Toric degenerations of cluster varieties and cluster duality, Gauss-Lusztig decomposition for positive quantum groups and representation by \(q\)-tori, The geometric \(R\)-matrix for affine crystals of type \(A\), Elementary Toda orbits and integrable lattices, A modification of the Anderson-Mirković conjecture for Mirković-Vilonen polytopes in types \(B\) and \(C\), Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths, Real Schubert Calculus: Polynomial Systems and a Conjecture of Shapiro and Shapiro, Totally positive matrices and dilogarithm identities, Plücker environments, wiring and tiling diagrams, and weakly separated set-systems, Cluster decorated geometric crystals, generalized geometric RSK-correspondences, and Donaldson-Thomas transformations, Planar flows and quadratic relations over semirings, Bott-Samelson atlases, total positivity, and Poisson structures on some homogeneous spaces, Mirković-Vilonen cycles and polytopes., Cluster algebras I: Foundations, Unnamed Item, Unnamed Item, Total positivity of a kind of generalized toric-Bernstein basis, Moduli spaces of local systems and higher Teichmüller theory, The \(\widehat {\mathfrak {sl}}(n)_k\)-WZNW fusion ring: a combinatorial construction and a realisation as quotient of quantum cohomology, Functional relations on anisotropic Potts models: from Biggs formula to the tetrahedron equation, Auslander-Reiten quivers and the Coxeter complex., With Wronskian through the looking Glass, Alcove random walks, \(k\)-Schur functions and the minimal boundary of the \(k\)-bounded partition poset, Tropical totally positive matrices, Tutte polynomials of vertex-weighted graphs and group cohomology, Cluster realizations of Weyl groups and higher Teichmüller theory, On Mirković-Vilonen cycles and crystal combinatorics, Locally convex curves and the Bruhat stratification of the spin group, In memoriam: Andrei Zelevinsky (1953--2013), Combinatorics of canonical bases revisited: type A, A survey on maximal green sequences, Stieltjes moment properties and continued fractions from combinatorial triangles, An order on circular permutations, Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians, Tropical planar networks, Alcove random walks and \(k\)-Schur functions, A plactic algebra action on bosonic particle configurations, Cluster algebras of finite type via Coxeter elements and principal minors., Flag manifolds over semifields, Supports for linear degenerations of flag varieties, Multiplicative properties of dual canonical bases of quantum groups, String cone and superpotential combinatorics for flag and Schubert varieties in type A, Affine type \(A\) geometric crystal on the Grassmannian, Total nonnegativity of GCD matrices and kernels, Generic bases for cluster algebras and the Chamber Ansatz, Soliton cellular automata associated with infinite reduced words, Regions of linearity, Lusztig cones, and canonical basis elements for the quantized enveloping algebra of type \(A_4\), Rectangle diagrams for the Lusztig cones of quantized enveloping algebras of type \(A\)., Double Bruhat cells and total positivity, Linear difference equations, frieze patterns, and the combinatorial Gale transform
