Perfect bases in representation theory: three mountains and their springs
From MaRDI portal
Publication:6119183
DOI10.4171/icm2022/132arXiv2201.02289OpenAlexW4389819232MaRDI QIDQ6119183
Publication date: 22 March 2024
Published in: International Congress of Mathematicians (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.02289
Combinatorial aspects of representation theory (05E10) Grassmannians, Schubert varieties, flag manifolds (14M15) Semisimple Lie groups and their representations (22E46) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Affine Mirković-Vilonen polytopes
- Crystals from categorified quantum groups
- Geometry of canonical bases and mirror symmetry
- Mirković-Vilonen cycles and polytopes.
- Polyhedra in the scheme space and the canonical basis in irreducible representations of \({\mathfrak gl}_ 3\)
- Global crystal bases of quantum groups
- Equivariant Chow groups for torus actions
- A polytope calculus for semisimple groups.
- Semicanonical bases arising from enveloping algebras
- Tensor product multiplicities, canonical and totally positive varieties
- Cluster algebras. III: Upper bounds and double Bruhat cells.
- Crystal bases and quiver varieties
- The Mirković-Vilonen basis and Duistermaat-Heckman measures
- Polyhedral parametrizations of canonical bases \& cluster duality
- The crystal structure on the set of Mirković-Vilonen polytopes
- Triangular bases in quantum cluster algebras and monoidal categorification conjectures
- Geometric Langlands duality and representations of algebraic groups over commutative rings
- Rigid modules over preprojective algebras.
- Crystalizing the q-analogue of universal enveloping algebras
- Coulomb branches of \(3d\) \(\mathcal{N}=4\) quiver gauge theories and slices in the affine Grassmannian
- Integral homology of loop groups via Langlands dual groups
- Rank 2 affine MV polytopes
- Canonical bases and KLR-algebras
- Generic bases for cluster algebras and the Chamber Ansatz
- Monoidal categorification of cluster algebras
- Cluster algebras IV: Coefficients
- Canonical Bases Arising from Quantized Enveloping Algebras
- A diagrammatic approach to categorification of quantum groups I
- Quivers with potentials and their representations II: Applications to cluster algebras
- Cluster ensembles, quantization and the dilogarithm
- Canonical Bases Arising from Quantized Enveloping Algebras. II
- Equivariant homology and K-theory of affine Grassmannians and Toda lattices
- On category O for affine Grassmannian slices and categorified tensor products
- Mirkovic-Vilonen polytopes and Khovanov-Lauda-Rouquier algebras
- Semicanonical bases and preprojective algebras
