7 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…
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…
Classification of irreducible real modules of real Lie superalgebras
Siddhartha Sahi, Hadi Salmasian, Vera Serganova
We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras afte…
Almost inner derivations of Lie superalgebras
Vera Serganova, Arkady Vaintrob
An almost inner derivation of a Lie algebra is a derivation that coincides with an inner derivation on each one-dimensional subspace of . The almost inner derivations form a…
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…
Sylow theorems for supergroups
Vera Serganova, Alexander Sherman, Dmitry Vaintrob
We introduce Sylow subgroups and -groups to the theory of complex algebraic supergroups, which mimic Sylow subgroups and -groups in the theory of finite groups. We prove that…
Quasireductive supergroups
Vera Serganova
We call an affine algebraic supergroup quasireductive if its underlying algebraic group is reductive. We obtain some results about the structure and representations of reductive su…