On an Infinite Limit of BGG Categories  O

Coulembier, Kevin; Penkov, Ivan

doi:10.17323/1609-4514-2019-19-4-655-693

Cited by 6 publications

(4 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since End O (π(P (λ))) ∼ = End O ν-pres (P (λ)), for any λ ∈ Λ(ν), is a local ring, it follows that π(P (λ)) is indecomposable in O by [Kr,Proposition 5.4]. Finally, it follows from [CP,Lemma A.1.3] that π(P (λ)) is projective in O. This completes the proof.…”

Section: Equivalence Of Categoriesmentioning

confidence: 92%

“…We are now in the position to invoke [CP,Lemma A.2.1] Hom g (P (λ), M ) (9.2) satisfies the universal property for the Serre quotient O. 9.3.…”

Section: Appendix a Structural Modules In O ν-Presmentioning

confidence: 99%

“…We record the following universal property of Serre quotient categories (see also [CP,Lemma A.1.2]).…”

Section: Equivalence Of Categoriesmentioning

confidence: 99%

See 2 more Smart Citations

Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras

Chen¹,

Cheng²,

Mazorchuk³

2022

Preprint

View full text Add to dashboard Cite

We study various categories of Whittaker modules over a type I Lie superalgebra realized as cokernel categories that fit into the framework of properly stratified categories. These categories are the target of the Backelin functor Γ ζ . We show that these categories can be described, up to equivalence, as Serre quotients of the BGG category O and of certain singular categories of Harish-Chandra (g, g0)bimodules. We also show that Γ ζ is a realization of the Serre quotient functor. We further investigate a q-symmetrized Fock space over a quantum group of type A and prove that, for general linear Lie superalgebras our Whittaker categories, the functor Γ ζ and various realizations of Serre quotients and Serre quotient functors categorify this q-symmetrized Fock space and its q-symmetrizer. In this picture, the canonical and dual canonical bases in this q-symmetrized Fock space correspond to tilting and simple objects in these Whittaker categories, respectively. Contents 1. Introduction 1 2. Preliminaries 6 3. Quantum groups and canonical bases 9 4. Equivalence of categories 17 5. Stratified structure of O 24 6. Tilting modules and Ringel duality 29 7. Categorification of the q-symmetrized Fock space 33 8. Appendix A. Structural modules in O ν-pres 41 9. Appendix B. A realization of O and its graded version. 43 References 47

show abstract

Section: Equivalence Of Categoriesmentioning

confidence: 92%

“…We are now in the position to invoke [CP,Lemma A.2.1] Hom g (P (λ), M ) (9.2) satisfies the universal property for the Serre quotient O. 9.3.…”

Section: Appendix a Structural Modules In O ν-Presmentioning

confidence: 99%

See 1 more Smart Citation

Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras

Chen¹,

Cheng²,

Mazorchuk³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Since this category is well understood by now, it is natural to look for analogues of category O for gl(∞). Several alternatives have been proposed such as those by Nampaisarn [Nam17], Coulembier and Penkov [CP19], and Penkov and Serganova [PS19].…”

Section: Introductionmentioning

confidence: 99%

Highest weight categories of $\mathfrak{gl}(\infty)$-modules

Zadunaisky¹

2022

Preprint

View full text Add to dashboard Cite

We study a category of modules over gl(∞) analogous to category O. We fix adequate Cartan, Borel and Levi-type subalgebras h, b and l with l ∼ = gl(∞) n , and define O l LA gl(∞) to be the category of h-semisimple, n-nilpotent modules that satisfy a large annihilator condition as l-modules. Our main result is that these are highest weight categories in the sense of Cline, Parshall and Scott. We compute the simple multiplicities of standard objects and the standard multiplicities in injective objects, and show that a form of BGG reciprocity holds in O l LA gl(∞). We also give a decomposition of O l LA gl(∞) into irreducible blocks.

show abstract

Weight Modules

Penkov

Hoyt

2021

Springer Monographs in Mathematics

View full text Add to dashboard Cite

On an Infinite Limit of BGG Categories O

Cited by 6 publications

References 13 publications

Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras

Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras

Highest weight categories of $\mathfrak{gl}(\infty)$-modules

Weight Modules

Contact Info

Product

Resources

About