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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).
J. Brundan and A. Kleshchev, Graded decomposition numbers for cyclotomic Hecke algebras, Advances Math
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S. Ariki, On the decomposition numbers of the Hecke algebra of G ( m , 1 , n ) G(m,1,n) , J. Math. Kyoto Univ
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J. J. Graham and G. I. Lehrer, Cellular algebras, Invent. Math
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R. Dipper, G. D. James and A. Mathas, Cyclotomic q q -Schur algebras, Math. Z
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A. Mathas, Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group
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S. Ariki and A. Mathas, The number of simple modules of the Hecke algebra of type G ( r , 1 , n ) G(r,1,n) , Math. Z
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G. D. James and A. Mathas, The Jantzen sum formula for cyclotomic q q -Schur algebras, Trans. Amer. Math. Soc
S. Ariki, Representations of Quantum Algebras and Combinatorics of Young Tableaux
2002
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C. Nǎstǎsescu and F. Van Oystaeyen, Methods of Graded Rings
2004
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A. Kleshchev, Linear and Projective Representations of Symmetric Groups
2005
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S. Ariki, A. Mathas and H. Rui, Cyclotomic Nazarov-Wenzl algebras, Nagoya Math. J
2006
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J. Brundan and A. Kleshchev, Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras, Invent. Math
2009
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M. Khovanov and A. Lauda, A diagrammatic approach to categorification of quantum groups I, Represent. Theory
2009
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2000
Cited alongside, same era.
Cited in the paper.
I. Grojnowski, Affine 𝔰 𝔩 p \mathfrak{sl}_{p} controls the representation theory of the symmetric group and related Hecke algebras; arXiv:math.RT/9907129
Cited in the paper.
R. Rouquier, 2 2 -Kac-Moody algebras; arXiv:0812.5023
Cited in the paper.