Type A blocks of super category <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">O</mml:mi></mml:math>

Brundan, Jonathan; Davidson, Nicholas

doi:10.1016/j.jalgebra.2016.11.022

Cited by 10 publications

(3 citation statements)

References 25 publications

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“…Despite the important early work done by Penkov-Serganova and others to obtain character formulas and other information (see [PS,Bru1] and references therein), the representation theory in type Q remain mysterious. For example, only very recently the structure of category O for q became clear thanks to the work of Chen [Che], Cheng-Kwon-Wang [CKW], and Brundan-Davidson [BD2,BD3].…”

Section: Introductionmentioning

confidence: 99%

A Basis Theorem for the Degenerate Affine Oriented Brauer–Clifford Supercategory

Brundan¹,

Comes²,

Kujawa³

2019

Can. J. Math.-J. Can. Math.

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We introduce the oriented Brauer-Clifford and degenerate affine oriented Brauer-Clifford supercategories. These are diagrammatically defined monoidal supercategories which provide combinatorial models for certain natural monoidal supercategories of supermodules and endosuperfunctors, respectively, for the Lie superalgebras of type Q. Our main results are basis theorems for these diagram supercategories. We also discuss connections and applications to the representation theory of the Lie superalgebra of type Q. 1

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Section: Introductionmentioning

confidence: 99%

A Basis Theorem for the Degenerate Affine Oriented Brauer–Clifford Supercategory

Brundan¹,

Comes²,

Kujawa³

2019

Can. J. Math.-J. Can. Math.

Self Cite

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“…Despite the important early work done by Penkov-Serganova, Brundan, and others to obtain character formulas and other information (see [26,3] and references therein), the representation theory in type Q remains mostly mysterious. For example, only very recently the structure of category O for q(n) became clear thanks to the work of Chen [13], Cheng-Kwon-Wang [14], and Brundan-Davidson [7,8].…”

mentioning

confidence: 99%

Webs of type Q

Brown¹,

Kujawa²

2022

Algebraic Combinatorics

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Howe dualities lead to diagrammatic categories which describe the representations of Lie-type objects as a monoidal category (that is, via generators and relations). Applying this philosophy to the type Q Howe duality of Cheng-Wang and Sergeev, we introduce diagrammatic web supercategories of type Q via generators and relations and show they describe the full subcategory of supermodules for the Lie superalgebra of type Q given by the tensor products of supersymmetric tensor powers of the natural supermodule.

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“…, λ n ) is a stacking of boxes, with λ 1 boxes in the first row, λ 2 boxes in the second row, etc, and the beginning of the i-th row is the i-th column. For example, the diagram associated to (4,3,2,1) is the following…”

mentioning

confidence: 99%

Two Boundary Centralizer Algebras for $\mathfrak{q}(n)$

Zhu

2019

Preprint

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We define the degenerate two boundary affine Hecke-Clifford algebra H d , and show it admits a well-defined q(n)-linear action on the tensor space M ⊗ N ⊗ V ⊗d , where V is the natural module for q(n), and M, N are arbitrary modules for q(n), the Lie superalgebra of Type Q. When M and N are irreducible highest weight modules parameterized by a staircase partition and a single row, respectively, this action factors through a quotient of H d . We then construct explicit modules for this quotient, H p,d , using combinatorial tools such as shifted tableaux and the Bratteli graph. These modules belong to a family of modules which we call calibrated. Using the relations in H p,d , we also classify a specific class of calibrated modules. The irreducible summands of M ⊗ N ⊗ V ⊗d coincide with the combinatorial construction, and provide a weak version of the Schur-Weyl type duality.

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Type A blocks of super category O

Cited by 10 publications

References 25 publications

A Basis Theorem for the Degenerate Affine Oriented Brauer–Clifford Supercategory

A Basis Theorem for the Degenerate Affine Oriented Brauer–Clifford Supercategory

Webs of type Q

Two Boundary Centralizer Algebras for $\mathfrak{q}(n)$

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