Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

Abstract

We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki's categorification theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial Z-grading on blocks of cyclotomic Hecke algebras, including symmetric groups in positive characteristic.

32 pages; minor changes to section 6

References in corpus (3)

• 2-Kac-Moody algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Blocks of cyclotomic Hecke algebras

Cited by in corpus (45)

• 2-Kac-Moody algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Categorifications from planar diagrammatics
• Modular representation theory in type A via Soergel bimodules
• Representations of the oriented skein category
• Trace as an alternative decategorification functor
• Schurian-finiteness of blocks of type $A$ Hecke algebras
• Universal construction of topological theories in two dimensions
• Graded dimensions and monomial bases for the cyclotomic quiver Hecke algebras
• A KLR Grading of the Brauer Algebras
• Cellularity and subdivision of KLR and weighted KLRW algebras
• The homology of the Temperley-Lieb algebras
• Graded induction for Specht modules
• Homogeneous representations of Type A KLR-algebras and Dyck paths
• Categorification of tensor product representations of sl(k) and category O
• Core blocks for Hecke algebras of type B and sign sequences
• Quiver Schur algebras and cohomological Hall algebras
• Skew cellularity of the Hecke algebras of type $G(\ell ,p,n)$
• Representations of orientifold Khovanov-Lauda-Rouquier algebras and the Enomoto-Kashiwara algebra
• Blob algebra and two-color Soergel calculus
• Content systems and deformations of cyclotomic KLR algebras of type $A$ and $C$
• The nil-blob algebra: An incarnation of type ${\tilde{A}}_1$ Soergel calculus and of the truncated blob algebra
• Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words
• Representation type of cyclotomic quiver Hecke algebras of type $A_{\ell }^{(1)}$
• Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
• Categorical crystals for quantum affine algebras
• An isomorphism theorem for degenerate cyclotomic Yokonuma-Hecke algebras and applications
• Seminormal bases of cyclotomic Hecke-Clifford algebras
• Knizhnik--Zamolodchikov functor for degenerate double affine Hecke algebras : algebraic theory
• A skew Specht perspective of RoCK blocks and cuspidal systems for KLR algebras in affine type A
• Path combinatorics and light leaves for quiver Hecke algebras
• Derived equivalences and sl_2-categorifications for U_q(gl_n)
• The Brundan-Kleshchev isomorphism revisited
• Decomposable Specht modules indexed by bihooks II
• Super duality for quantum affine algebras of type $A$
• Representation type of higher level cyclotomic quiver Hecke algebras in affine type C
• Enhanced nilHecke algebras and baby Verma modules
• Cellularity of KLR and weighted KLRW algebras via crystals
• An interpretation of the Lascoux-Leclerc-Thibon algorithm and graded representation theory
• Representation Theory of Symmetric Groups and Related Hecke Algebras
• Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups
• Trace and categorical sl(n) representations
• sl_2-actions along short strings for spin blocks
• Representations of cyclotomic oriented Brauer categories
• The Brundan-Kleshchev subalgebra and BK-type isomorphsims