Graded decomposition numbers for cyclotomic Hecke algebras

By Jonathan Brundan, Alexander S. Kleshchev. 2009

215 citations recorded by the source corpus.

Abstract In recent joint work with Wang, we have constructed graded Specht modules for cyclotomic Hecke algebras. In this article, we prove a graded version of the Lascoux–Leclerc–Thibon conjecture, describing the decomposition numbers of graded Specht modules over a field of characteristic zero.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/07208aa3c96c153bcaa7db821fc92a6ab62d630c

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quiver Hecke Algebras and 2-Lie Algebras (2011, methodology): “c2(E) "" E E E E E E E E π∗ΛY xy // π∗ΛY [4] T // π∗ΛY [2]”
Universal graded Specht modules for cyclotomic Hecke algebras (2011, background): “Moreover, Brundan, Kleshchev and Wang [6] show that the Specht modules over F can be graded, which plays a crucial role in the graded categorification theorem of Brundan and Kleshchev [4], thus generalizing Ariki’s categorification theorem [1].”
Canonical bases and higher representation theory (2012, background): “92]. •Lascoux, Leclerc andThibon[LLT96]show that alevel1Fock spacerepresentationofbsl n carriesacanonicalbasis. Thiswasextendedtohigherleveltwisted Fock spaces by Uglov [Ugl00]; Brundan and Kleshchev [BK09a] showed that tensor products of level 1 Fock spaces also have a canonical basis arising as a ”
Implicit structure in 2-representations of quantum groups (2011, methodology): “n). IMPLICIT STRUCTURE IN 2-REPRESENTATIONS OF QUANTUM GROUPS 33 7.4.2. Brundan-Kleshchev. Brundan and Kleshchev gave an algebraic proof of the cyclotomic quotient conjecture for g = sl∞ and g = csle [3] with choice of scalars Q determined from an orientation of the quiver. Their work uses an isomor”
Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words (2009, background): “Categorification of fA and f ∗ A .”
Crystals from categorified quantum groups (2009, background): “The more general conjecture was proven in finite and affine type A by Brundan and Kleshchev [BK08, BK09].”
Categorifications from planar diagrammatics (2010, background): “For instance, key results about simple and projective R(ν)-modules [26] follow via Kleshchev-Grojnowski constructions that amount to the representation-theoretical counterpart of the crystal graph structure.”
Graded Specht modules (2009, background): “The first two authors have recently found a proof of the graded version of the conjecture too, starting from Ariki’s theorem; see [8].”