1 citations · 3 across the 12 of their papers we have counts for
16 papers
The Harish-Chandra isomorphism for supersymmetric spaces and ghost distributions
Shifra Reif, Siddhartha Sahi, Vera Serganova +1
We prove the Harish-Chandra isomorphism theorem for supersymmetric spaces, describing the polynomial algebra of eigenvalues of invariant differential operators. The polynomials obt…
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…
Localization theorem for homological vector fields
Vera Serganova, Alexander Sherman
We present a general theorem which computes the cohomology of a homological vector field on global sections of vector bundles over smooth affine supervarieties. The hypotheses and…
Ghost distributions on supersymmetric spaces II: basic classical superalgebras
Alexander Sherman
We study ghost distributions on supersymmetric spaces for the case of basic classical Lie superalgebras. We introduce the notion of interlaced pairs, which are those for which both…
On the Grothendieck ring of a quasireductive Lie superalgebra
Maria Gorelik, Vera Serganova, Alexander Sherman
Given a Lie superalgebra and a maximal quasitoral subalgebra , we consider properties of restrictions of -modules to . This…
Splitting quasireductive supergroups and volumes of supergrassmannians
Vera Serganova, Alexander Sherman
We introduce the notion of splitting subgroups of quasireducitve supergroups, and explain their significance. For , , and defect one basic classical supergroups, we…
On the Duflo-Serganova functor for the queer Lie superalgebra
Maria Gorelik, Alexander Sherman
We study the Duflo-Serganova functor for the queer Lie superalgebra and for all odd with semisimple. For the case when the rank o…
The Duflo-Serganova functor, vingt ans après
Maria Gorelik, Crystal Hoyt, Vera Serganova +1
We review old and new results concerning the functor and associated varieties for Lie superalgebras. These notions were introduced in the unpublished manuscript arXiv:math/050…
On symmetries of the Duflo-Serganova functor
Alexander Sherman
We discuss several points regarding symmetries of the Duflo-Serganova functor. In particular we give new constructions of Lie superalgebras, Lie supergroups, and associative supera…
Ghost distributions on supersymmetric spaces I: Koszul induced superspaces, branching, and the full ghost centre
Alexander Sherman
Given a Lie superalgebra , Gorelik defined the anticentre of its enveloping algebra, which consists of certain elements that square to the center. We se…
Two geometric proofs of the classification of algebraic supergroups with semisimple representation theory
Alexander Sherman
We present two novel proofs of the known classification of connected affine algebraic supergroups such that is semisimple. The proofs are geometrically mo…
Iwasawa Decomposition for Lie Superalgebras
Alexander Sherman
Let be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and an involution of preserving a nondegenerate…
Layers of the Coradical Filtration
Alexander Sherman
Under suitably nice conditions, given a coalgebra object in a tensor category we compute the layers of its coradical (socle) filtration.
Spherical Supervarieties
Alexander Sherman
We give a definition of the notion of spherical varieties in the world of complex supervarieties with actions of algebraic supergroups. A characterization of affine spherical super…
Spherical Indecomposable Representations of Lie Superalgebras
Alexander Sherman
We present a classification of all spherical indecomposable representations of classical and exceptional Lie superalgebras. We also include information about stabilizers, symmetric…
Omitting types and AF algebras
Kevin Carlson, Enoch Cheung, Ilijas Farah +5
We give model-theoretic characterizations of UHF algebras and of AF algebras as C*-algebras that omit certain sets of types.