Graded Specht modules

By Jonathan Brundan, Alexander S. Kleshchev, Weiqiang Wang. 2009

132 citations recorded by the source corpus.

Abstract Recently, the first two authors have defined a ℤ-grading on group algebras of symmetric groups and more generally on the cyclotomic Hecke algebras of type G(l, 1, d). In this paper we explain how to grade Specht modules over these algebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/499cdc2b3bd3c53c0175241b3fa88442b4956122

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Citations in the corpus

Universal graded Specht modules for cyclotomic Hecke algebras (2011, methodology): “23 when we show that these universal graded Specht modules are isomorphic to the usual graded Specht modules from [6, 10].”
Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras (2008, methodology): “ predicted already by Rouquier [R1, Remark 3.11] and Turner [T]. This means that it is now possible to study graded representation theory of these algebras. First steps in this direction are taken in [BKW], in which we construct graded versions of Specht modules. Corollary 2 can be viewed as an exte”
Highest weight categories arising from Khovanov's diagram algebra III: category O (2008, methodology): “This follows from Lemma 9.3 using Corollary 8.20 and the fact that Eα(V(λ)) ∼= V(λ) by Corollary 8.19. Corollary 9.6. For any λ∈ Γ, the cell module S(λ) is isomorphic to the graded Specht module from [BKW] parametrized by the bipartition obtained from λby applying the map from Remark 2.1 (taking e :”
Categorifications from planar diagrammatics (2010, background): “somorphism. To get this match, when Γ has an odd length cycle, the deﬁnition of R(ν) should be slightly modiﬁed, see the above references and [27, 44]. Rings R(ν) proved handy in recent constructions [7, 9, 2] of graded versions of the group algebra of Sn, Specht modules, and q-Schur algebras, also ”
Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A (2009, background): “Brundan, Kleshchev and Wang [8] actually define the graded left module S∗λ BKW , however, it is an easy exercise to switch their notation to the right.”
Crystals from categorified quantum groups (2009, background): “This has led to the definition of graded Specht modules for cyclotomic Hecke algebras [11], the construction of a homogeneous cellular basis for the cyclotomic quotients R(ν) in type A [22], the introduction of gradings in the study of q-Schur algebras [4], and an extension of the generalized LLT co”
Representation theory of symmetric groups and related Hecke algebras (2009, methodology): “, 114] and Rouquier [174]. The Khovanov-Lauda-Rouquier algebras are naturally Z-graded, so combining with our isomorphism, we obtain an explicit grading on the blocks of cyclotomic Hecke algebras. In [42] we then grade Specht modules, which allows us to deﬁne graded decomposition numbers. Finally, i”