Results 1  10
of
87
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 ..."
Abstract

Cited by 103 (12 self)
 Add to MetaCart
(Show Context)
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
Dual canonical Bases, quantum Shuffles and qCharacters
, 2003
"... Rosso and Green have shown how to embed the positive part Uq(n) of a quantum enveloping algebra Uq(g) in a quantum shuffle algebra. In this paper we study some properties of the image of the dual canonical basis B ∗ of Uq(n) under this embedding Φ. This is motivated by the fact that when g is of typ ..."
Abstract

Cited by 29 (3 self)
 Add to MetaCart
Rosso and Green have shown how to embed the positive part Uq(n) of a quantum enveloping algebra Uq(g) in a quantum shuffle algebra. In this paper we study some properties of the image of the dual canonical basis B ∗ of Uq(n) under this embedding Φ. This is motivated by the fact that when g is of type Ar, the elements of Φ(B ∗ ) are qanalogues of irreducible characters of the affine IwahoriHecke algebras attached to the groups GL(m) over a padic field.
Super duality and irreducible characters of orthosymplectic Lie superalgebras
 Invent. Math
"... ar ..."
(Show Context)
Cohomology of generalized supergrassmannians and character formulae for basic classical
, 906
"... Lie superalgebras ..."
(Show Context)
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 ..."
Abstract

Cited by 27 (14 self)
 Add to MetaCart
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.
Howe Duality for Lie Superalgebras
 COMPOSITIO MATH
, 2000
"... We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicityfree decomposition of a symmetric and skewsymmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each ..."
Abstract

Cited by 26 (7 self)
 Add to MetaCart
(Show Context)
We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicityfree decomposition of a symmetric and skewsymmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each isotypic subspace of the symmetric algebra. We give an explicit multiplicityfree decomposition into irreducible gl(mn)modules of the symmetric and skewsymmetric algebras of the symmetric square of the natural representation of gl(mn). In the former case we find as well explicit formulas for the highest weight vectors. Our work unifies and generalizes the classical results in symmetric and skewsymmetric models and admits several applications.
CHARACTER AND DIMENSION FORMULAE FOR GENERAL LINEAR SUPERALGEBRA
, 2004
"... Abstract. The generalized KazhdanLusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of composition factors of an arbitrary rfold atypical gl ..."
Abstract

Cited by 23 (4 self)
 Add to MetaCart
(Show Context)
Abstract. The generalized KazhdanLusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of composition factors of an arbitrary rfold atypical gl mnKacmodule and the set of composition factors of some rfold atypical gl rrKacmodule. The result of KazhdanLusztig polynomials is also applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the KacWeyl form, and derive from it a closed formula for the dimension of any finite dimensional irreducible representation of the general linear superalgebra. 1.
Constructible characters and canonical bases
, 2003
"... We give closed formulas for all vectors of the canonical basis of a level 2 irreducible integrable representation of Uv(sl∞). These formulas coincide at v = 1 with Lusztig’s formulas for the constructible characters of the IwahoriHecke algebras of type B and D. 1 ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
(Show Context)
We give closed formulas for all vectors of the canonical basis of a level 2 irreducible integrable representation of Uv(sl∞). These formulas coincide at v = 1 with Lusztig’s formulas for the constructible characters of the IwahoriHecke algebras of type B and D. 1
Irreducible characters of general linear superalgebra and super duality
, 2009
"... We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finitedimensional modules, by directly relating the problem to the classical KazhdanLusztig theory. We further verify a parabolic version of a conj ..."
Abstract

Cited by 20 (6 self)
 Add to MetaCart
We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finitedimensional modules, by directly relating the problem to the classical KazhdanLusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category O of the general linear superalgebra. We also prove the super duality conjecture.