Categorical actions and crystals

Brundan, Jonathan; Davidson, Nicholas

doi:10.1090/conm/683/13724

Cited by 17 publications

(46 citation statements)

References 35 publications

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“…The equivalence of our definition with the Losev-Webster definition may be verified by a similar argument to the one explained in [BLW,Remark 2.11]. Hence, we obtain the following as a special case of the uniqueness theorem for TPCs that is the main result of [LW]; we refer to [BD2,Definition 4.7] for the definition of strongly equivariant equivalence being used here.…”

Section: 2supporting

confidence: 64%

“…The proof of the uniqueness theorem in [LW] gives a great deal of additional information about the structure of TPCs of V ⊗n k . In particular, [LW,Theorem 7.2] gives an explicit combinatorial description of the associated crystal in the general sense of [BD2,§4.4]. Also, [LW,Proposition 5.2] gives a classification of the indecomposable prinjective (= projective and injective) objects.…”

Section: 2mentioning

confidence: 99%

“…This is enough to show that Q is fully faithful; cf. [BD2,Lemma 2.13]. It just remains to show that Q is dense.…”

Section: 2mentioning

confidence: 99%

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Type A blocks of super category O

Brundan¹,

Davidson²

2017

Journal of Algebra

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We show that the blocks of category O for the Lie superalgebra qn(C) associated to half-integral weights carry the structure of a tensor product categorification for the infinite rank Kac-Moody algebra of type C∞. This allows us to prove two conjectures formulated by Cheng, Kwon and Lam. We then focus on the full subcategory consisting of finite-dimensional representations, which we show is a highest weight category with blocks that are Morita equivalent to certain generalized Khovanov arc algebras.

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Section: 2supporting

confidence: 64%

Section: 2mentioning

confidence: 99%

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Type A blocks of super category O

Brundan¹,

Davidson²

2017

Journal of Algebra

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“…In , Webster has proposed a proof of the Nondegeneracy Conjecture for all purely even types. There is also a completely different proof of the Decategorification Conjecture based on results of , which is valid in all finite types; see, for example, [, Corollary 4.21].…”

Section: Introductionmentioning

confidence: 99%

Super Kac–Moody 2‐categories

Brundan

Ellis

2017

Proc. London Math. Soc.

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“…The following is the quantum analog of [B1, Lemma 1.8]; see also [BD, Lemma 4.14] for the analog in the setting of Kac-Moody 2-categories.…”

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confidence: 99%

On the definition of Heisenberg category

Brundan¹

2018

Algebraic Combinatorics

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We introduce a diagrammatic monoidal category Heis k (z, t) which we call the quantum Heisenberg category; here, k ∈ Z is "central charge" and z and t are invertible parameters. Special cases were known before: for central charge k = −1 and parameters z = q − q −1 and t = −z −1 our quantum Heisenberg category may be obtained from the deformed version of Khovanov's Heisenberg category introduced by Licata and the second author by inverting its polynomial generator, while Heis 0 (z, t) is the affinization of the HOMFLY-PT skein category. We also prove a basis theorem for the morphism spaces in Heis k (z, t).

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Categorical actions and crystals

Abstract: This is an expository article developing some aspects of the theory of categorical actions of Kac-Moody algebras in the spirit of works of Chuang-Rouquier, Khovanov-Lauda, Webster, and many others.

Cited by 17 publications

References 35 publications

Type A blocks of super category O

Type A blocks of super category O

Super Kac–Moody 2‐categories

On the definition of Heisenberg category

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