21 citations · 79 across the 16 of their papers we have counts for
21 papers
Balanced and neat elements in quasi-reductive Lie superalgebras
Inna Entova-Aizenbud, Vera Serganova
Let be a quasi-reductive supergroup (so its underlying algebraic group is reductive). We consider two trivially intersecting classes of odd elements: neat elements…
Towards the Green correspondence for supergroups
Inna Entova-Aizenbud, Vera Serganova, Alex Sherman
We prove a version of the Green correspondence for complex algebraic supergroups, constructing a correspondence between certain indecomposable representations of G and the normaliz…
Deligne-Knop tensor categories and functoriality
Inna Entova-Aizenbud, Thorsten Heidersdorf
A general construction of Knop creates a symmetric monoidal category from any regular category and a fixed degree function . A special…
It takes two spectral sequences
Inna Entova-Aizenbud, Vera Serganova, Alexander Sherman
We study the representation theory of the Lie superalgebra , constructing two spectral sequences which eventually annihilate precisely the superdimension zero i…
Deligne categories and representations of the finite general linear group, part 1: universal property
Inna Entova-Aizenbud, Thorsten Heidersdorf
We study the Deligne interpolation categories for , first introduced by F. Knop. These categories interpolate the…
McKay trees
Avraham Aizenbud, Inna Entova-Aizenbud
Given a finite group and its representation , the corresponding McKay graph is a graph whose vertices are the irreducible representations of ; the number of edge…
Jacobson-Morozov Lemma for Algebraic Supergroups
Inna Entova-Aizenbud, Vera Serganova
Given a quasi-reductive algebraic supergroup , we use the theory of semisimplifications of symmetric monoidal categories to define a symmetric monoidal functor $Φ_x: Rep(G) \to…
Semisimplification of the category of tilting modules for GL_n
Jonathan Brundan, Inna Entova-Aizenbud, Pavel Etingof +1
We describe the semisimplification of the monoidal category of tilting modules for the algebraic group GL_n in characteristic p > 0. In particular, we compute the dimensions of the…
Monoidal abelian envelopes and a conjecture of Benson--Etingof
Kevin Coulembier, Inna Entova-Aizenbud, Thorsten Heidersdorf
We give several criteria to decide whether a given tensor category is the abelian envelope of a fixed symmetric monoidal category. As a main result we prove that the category of fi…
Duflo-Serganova functor and superdimension formula for the periplectic Lie superalgebra
Inna Entova-Aizenbud, Vera Serganova
In this paper, we study the representations of the periplectic Lie superalgebra using the Duflo-Serganova functor. Given a simple -module and a certain element…
Kac-Wakimoto conjecture for the periplectic Lie superalgebra
Inna Entova-Aizenbud, Vera Serganova
We prove the Kac-Wakimoto conjecture for the periplectic Lie superalgebra , stating that any simple module lying in a block of non-maximal atypicality has superdim…
Deligne categories and the periplectic Lie superalgebra
Inna Entova-Aizenbud, Vera Serganova
We study stabilization of finite-dimensional representations of the periplectic Lie superalgebras as . The paper gives a construction of the tensor…
The affine VW supercategory
Martina Balagovic, Zajj Daugherty, Inna Entova-Aizenbud +7
We define the affine VW supercategory , which arises from studying the action of the periplectic Lie superalgebra $\mathfrak{p}(…
Deligne categories and representations of the infinite symmetric group
Daniel Barter, Inna Entova-Aizenbud, Thorsten Heidersdorf
We establish a connection between two settings of representation stability for the symmetric groups over . One is the symmetric monoidal category ${\rm Rep}(S_{\i…
Translation functors and decomposition numbers for the periplectic Lie superalgebra
Martina Balagovic, Zajj Daugherty, Inna Entova-Aizenbud +7
We study the category of finite-dimensional integrable representations of the periplectic Lie superalgebra . We define an action of the Temperley--…
Categorical actions and multiplicities in the Deligne category
Inna Entova-Aizenbud
We study the categorical type A action on the Deligne category (here ) and its "abelian envelope" constructe…
Deligne categories and the limit of categories
Inna Entova-Aizenbud, Vladimir Hinich, Vera Serganova
For each integer a tensor category is constructed, such that exact tensor functors classify dualizable -dimensional objects in not annihila…
Notes on Restricted Inverse Limits of Categories
Inna Entova-Aizenbud
We describe the framework for the notion of a restricted inverse limit of categories, with the main motivating example being the category of polynomial representations of the group…
Deligne categories and reduced Kronecker coefficients
Inna Entova-Aizenbud
The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups; namely, given three partitions of , the m…
Schur-Weyl duality for Deligne categories
Inna Entova-Aizenbud
This paper gives an analogue to the classical Schur-Weyl duality in the setting of Deligne categories. Given a finite-dimensional unital vector space V (i.e. a vector space V with…
On representations of rational Cherednik algebras in complex rank
Inna Entova-Aizenbud
We study a family of abelian categories O_{c, t} depending on complex parameters c, t which are interpolations of the O-category for the rational Cherednik algebra H_c(t) of type A…