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Highest weight categories arising from Khovanov's diagram algebra II: Koszulity
"... This is the second of a series of four articles studying various generalisations of Khovanov’s diagram algebra. In this article we develop the general theory of Khovanov’s diagrammatically defined “projective functors” in our setting. As an application, we give a direct proof of the fact that the ..."
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Cited by 103 (12 self)
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This is the second of a series of four articles studying various generalisations of Khovanov’s diagram algebra. In this article we develop the general theory of Khovanov’s diagrammatically defined “projective functors” in our setting. As an application, we give a direct proof of the fact that the
A super duality and KazhdanLusztig polynomials
, 2004
"... We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A), via the canonical and dual canonical bases on Fock spaces which in turn may be seen as a reformulation of the KazhdanLusztig theory. As a consequence, the usual parabolic Kazhdan ..."
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Cited by 27 (14 self)
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We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A), via the canonical and dual canonical bases on Fock spaces which in turn may be seen as a reformulation of the KazhdanLusztig theory. As a consequence, the usual parabolic KazhdanLusztig polynomials of type A compute the characters of finitedimensional irreducible modules of the general linear Lie superalgebra.
The CalogeroMoser partition and Rouquier families for complex reflection groups
 J. Algebra
"... Abstract. Let W be a complex reflection group. We formulate a conjecture relating blocks of the corresponding restricted rational Cherednik algebras and Rouquier families for cyclotomic Hecke algebras. We verify the conjecture in the case that W is a wreath product of a symmetric group with a cyclic ..."
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Cited by 11 (4 self)
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Abstract. Let W be a complex reflection group. We formulate a conjecture relating blocks of the corresponding restricted rational Cherednik algebras and Rouquier families for cyclotomic Hecke algebras. We verify the conjecture in the case that W is a wreath product of a symmetric group with a cyclic group of order l. 1.
Crystal isomorphisms for irreducible highest weight Uv( sle)  modules of higher level
, 2007
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CRYSTAL GRAPHS OF IRREDUCIBLE Uv ( ̂ sle)MODULES OF LEVEL TWO AND UGLOV BIPARTITIONS
, 2006
"... Abstract. We give a simple description of the natural bijection between the set of FLOTW bipartitions and the set of Uglov bipartitions (which generalizes the set of Kleshchev bipartitions). These bipartitions, which label the crystal graphs of irreducible Uv ( ̂ sle)modules of level two, naturall ..."
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Cited by 5 (1 self)
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Abstract. We give a simple description of the natural bijection between the set of FLOTW bipartitions and the set of Uglov bipartitions (which generalizes the set of Kleshchev bipartitions). These bipartitions, which label the crystal graphs of irreducible Uv ( ̂ sle)modules of level two, naturally appear in the context of the modular representation theory of Hecke algebras of type Bn. 1.
Constructible representations and basic sets in type Bn
"... Abstract. We study the parametrizations of simple modules provided by the theory of basic sets for all finite Weyl groups. In the case of type Bn, we show the existence of basic sets for the matrices of constructible representations. Then we study bijections between the various basic sets and show t ..."
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Cited by 4 (3 self)
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Abstract. We study the parametrizations of simple modules provided by the theory of basic sets for all finite Weyl groups. In the case of type Bn, we show the existence of basic sets for the matrices of constructible representations. Then we study bijections between the various basic sets and show that they are controlled by the matrices of the constructible representations.
Factorization of the canonical bases for higher level Fock spaces
 Eding. Math. Soc
"... Abstract. The level l Fock space admits canonical bases Ge and G∞. They correspond to Uv(ŝle) and Uv(sl∞)module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in N[v]. Restriction to the highest weight modules generated by the emp ..."
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Cited by 4 (2 self)
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Abstract. The level l Fock space admits canonical bases Ge and G∞. They correspond to Uv(ŝle) and Uv(sl∞)module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in N[v]. Restriction to the highest weight modules generated by the empty lpartition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to ArikiKoike algebras. 1.
The CalogeroMoser partition for wreath products
"... Abstract. Let W be the wreath product of a symmetric group with a cyclic group of order l. The corresponding restricted rational Cherednik algebra is a finite dimensional algebra whose block structure has a combinatorial description in terms of Jhearts. We show that this description is equivalent t ..."
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Abstract. Let W be the wreath product of a symmetric group with a cyclic group of order l. The corresponding restricted rational Cherednik algebra is a finite dimensional algebra whose block structure has a combinatorial description in terms of Jhearts. We show that this description is equivalent to one given in terms of residues of multipartitions. This establishes links with Rouquier families for the associated cyclotomic Hecke algebra and deformed higher level Fock spaces. 1.
FACTORIZATION OF THE CANONICAL BASES FOR HIGHEST WEIGHT MODULES IN AFFINE TYPE A
, 909
"... Abstract. We show that the canonical basis associated to any highest weight Uv ( c sle)module can be decomposed on the canonical basis of its corresponding Uv(sl∞)module. We establish that the transition matrix associated to this decomposition is unitriangular with coefficients in Z[v] and give a ..."
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Abstract. We show that the canonical basis associated to any highest weight Uv ( c sle)module can be decomposed on the canonical basis of its corresponding Uv(sl∞)module. We establish that the transition matrix associated to this decomposition is unitriangular with coefficients in Z[v] and give a procedure to compute them. We conjecture these coefficients are in fact in N[v]. This provides a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices associated to ArikiKoike algebras. 1.