10 citations · 18 across the 9 of their papers we have counts for
14 papers · 1 filter
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…
Restriction Theorems and Root Systems for Symmetric Superspaces
Shifra Reif, Siddhartha Sahi, Vera Serganova
In this paper we consider those involutions of a finite-dimensional Kac-Moody Lie superalgebra , with associated decomposition $\mathfrak g=\mathfrak k\oplus\mathf…
Grothendieck Rings of Queer Lie Superalgebras
Shifra Reif
We determine the Grothendieck rings of the category of finite-dimensional modules over Queer Lie superalgebras via their rings of characters. In particular, we show that the ring o…
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}…
Denominator identities for the periplectic Lie superalgebra
Crystal Hoyt, Mee Seong Im, Shifra Reif
We prove denominator identities for the periplectic Lie superalgebra , thereby completing the problem of finding denominator identities for all simple classical fi…
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…
On tensor products of irreducible integrable representations
Shifra Reif, R. Venkatesh
We consider integrable category representations of Borcherds--Kac--Moody algebras whose Cartan matrix is finite dimensional, and determine the necessary and sufficien…
Grothendieck rings for Lie superalgebras and the Duflo-Serganova functor
Crystal Hoyt, Shifra Reif
We show that the Duflo-Serganova functor on the category of finite-dimensional modules over a finite-dimensional contragredient Lie superalgebra induces a ring homomorphism on a na…
A superdimension formula for gl(m|n) modules
Michael Chmutov, Rachel Karpman, Shifra Reif
We give a formula for the superdimension of a finite-dimensional simple gl(m|n)-module using the Su-Zhang character formula. As a corollary, we obtain a simple algebraic proof of a…
A Weyl-Type character formula for PDC modules of gl(m|n)
Michael Chmutov, Crystal Hoyt, Shifra Reif
In 1994, Kac and Wakimoto suggested a generalization of Bernstein and Leites character formula for basic Lie superalgebras, and the natural question was raised: to which simple hig…
Kac-Wakimoto character formula for the general linear Lie superalgebra
Michael Chmutov, Crystal Hoyt, Shifra Reif
Character formulas for Lie superalgebras have been shown to have important applications to number theory and combinatorics. We prove the Kac-Wakimoto character formula for the gene…
Denominator Identity for Twisted Affine Lie Superalgebras
Shifra Reif
The study of denominator identities for Lie superalgebras was recently developed by M. Gorelik, V.G. Kac, P.Moseneder Frajria, I. Musson, P. Papi, M. Wakimoto and the author. In th…
Denominator identity for affine Lie superalgebras with zero dual Coxeter number
Maria Gorelik, Shifra Reif
We prove a denominator identity for non-twisted affine Lie superalgebras with zero dual Coxeter number.
Simplicity of vacuum modules over affine Lie superalgebras
Crystal Hoyt, Shifra Reif
We prove an explicit condition on the level for the irreducibility of a vacuum module over a (non-twisted) affine Lie superalgebra, which was conjectured by M. Gorelik…