56 citations · 329 across the 50 of their papers we have counts for
9 papers · 2 filters
Capelli operators for spherical superharmonics and the Dougall-Ramanujan identity
Siddhartha Sahi, Hadi Salmasian, Vera Serganova
Let be an orthosympectic -graded vector space and let denote the Lie superalgebra of similitudes of . When the space…
The Grothendieck ring of the periplectic Lie supergroup and supersymmetric functions
Mee Seong Im, Shifra Reif, Vera Serganova
We show that the Grothendieck ring of finite-dimensional representations of the periplectic Lie supergroup is isomorphic to the ring of symmetric polynomials in $x_1^{\pm 1}…
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…
Tensor product of the Fock representation with its dual and the Deligne category
Vera Serganova
We describe the structure of the tensor product of the basic Fock representation of sl(\infty) with its shifted dual. More precisely we prove that this tensor product has a unique…
Snowflake modules and Enright functor for Kac-Moody superalgebras
Maria Gorelik, Vera Serganova
We introduce a class of modules over Kac-Moody superalgebras; we call these modules snowflake. These modules are characterized by invariance property of their characters with respe…
Grothendieck rings of periplectic Lie superalgebras
Mee Seong Im, Shifra Reif, Vera Serganova
We describe explicitly the Grothendieck rings of finite-dimensional representations of the periplectic Lie superalgebras. In particular, the Grothendieck ring of the Lie supergroup…
Representations of simple Jordan superalgebras
Iryna Kashuba, Vera Serganova
This paper completes description of categories of representations of finite-dimensional simple unital Jordan superalgebras over algebraically closed field of characteristic zero.
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…
Representations of principal -algebra for the superalgebra and the super Yangian
Elena Poletaeva, Vera Serganova
We classify irreducible representations of finite -algebra of the queer Lie superalgebra associated with the principal nilpotent coadjoint orbits. We use this classificat…