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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 These notions were introduced in the unpublished manuscript arXiv:math/050…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…