Lattice structure of Weyl groups via representation theory of preprojective algebras

DOI10.1112/S0010437X18007078zbMath1443.16016arXiv1604.08401OpenAlexW3104735982WikidataQ105553914 ScholiaQ105553914MaRDI QIDQ4683887

Hugh Thomas, Osamu Iyama, Idun Reiten, Nathan Reading

Publication date: 26 September 2018

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.08401

zbMATH Keywords

Weyl group\(\tau\)-tilting theoryweak orderpreprojective algebrajoin-irreducible elementlattice congruencebrick

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Torsion theories, radicals (18E40) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Representations of associative Artinian rings (16G10) Lattice ideals, congruence relations (06B10)

Related Items (25)

The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders ⋮ On the module categories of generalized preprojective algebras of Dynkin type ⋮ Two-term tilting complexes for preprojective algebras of non-Dynkin type ⋮ Classifying torsion classes for algebras with radical square zero via sign decomposition ⋮ Lattice theory of torsion classes: Beyond 𝜏-tilting theory ⋮ Biclosed sets in affine root systems ⋮ Morphisms and extensions between bricks over preprojective algebras of type A ⋮ Wide subcategories and lattices of torsion classes ⋮ Weak orders on symmetric groups and posets of support τ-tilting modules ⋮ The canonical join complex ⋮ Bricks over preprojective algebras and join-irreducible elements in Coxeter groups ⋮ \(\tau\)-rigid modules over Auslander algebras ⋮ Pairwise compatibility for 2-simple minded collections ⋮ Classifying \(\tau\)-tilting modules over the Auslander algebra of \(K[x/(x^n)\)] ⋮ Lattice bijections for string modules, snake graphs and the weak Bruhat order ⋮ Stability, shards, and preprojective algebras ⋮ Dynamical combinatorics and torsion classes ⋮ Bigrassmannian permutations and Verma modules ⋮ The fundamental theorem of finite semidistributive lattices ⋮ A survey on maximal green sequences ⋮ Exceptional sequences and spherical modules for the Auslander algebra of \(k[x/(x^t)\)] ⋮ Arc diagrams and 2-term simple-minded collections of preprojective algebras of type \(A\) ⋮ Minimal inclusions of torsion classes ⋮ Pairwise compatibility for 2-simple minded collections. II: Preprojective algebras and semibrick pairs of full rank ⋮ Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras

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