S. Sahi

activity

19962026

most citedA recursion and a combinatorial formula for Jack polynomials

215 citations · 550 across the 60 of their papers we have counts for

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29 papers · 1 filter

math.RT2026

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…

math.RT2026

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…

math.RT2024

Restriction Theorems and Root Systems for Symmetric Superspaces

Shifra Reif, Siddhartha Sahi, Vera Serganova

In this paper we consider those involutions $θ$ of a finite-dimensional Kac-Moody Lie superalgebra $g$ , with associated decomposition $\mathfrak g=\mathfrak k\oplus\mathf…

math.RT2023★ 1 cited

Eigenvalues of supersymmetric Shimura operators and interpolation polynomials

Siddhartha Sahi, Songhao Zhu

The Shimura operators are a certain distinguished basis for invariant differential operators on a Hermitian symmetric space. Answering a question of Shimura, Sahi and Zhang showed…

math.RT2022

Quasi-polynomial representations of double affine Hecke algebras

Siddhartha Sahi, Jasper Stokman, Vidya Venkateswaran

We introduce an explicit family of representations of the double affine Hecke algebra $H$ acting on spaces of quasi-polynomials, defined in terms of truncated Demazure-Lus…

math.RT2022

A Stone-von Neumann equivalence of categories for smooth representations of the Heisenberg group

Raul Gomez, Dmitry Gourevitch, Siddhartha Sahi

The classical Stone-von Neuman theorem relates the irreducible unitary representations of the Heisenberg group $H_{n}$ to non-trivial unitary characters of its center $Z$ , and plays…

math.RT2022★ 1 cited

From Cauchy's determinant formula to bosonic and fermionic immanant identities

Apoorva Khare, Siddhartha Sahi

Cauchy's determinant formula (1841) involving $det ((1 - u_{i} v_{j})^{- 1})$ is a fundamental result in symmetric function theory. It has been extended in several directions, including…

math.RT2019

Capelli operators for spherical superharmonics and the Dougall-Ramanujan identity

Siddhartha Sahi, Hadi Salmasian, Vera Serganova

Let $(V, ω)$ be an orthosympectic $Z_{2}$ -graded vector space and let $g := gosp (V, ω)$ denote the Lie superalgebra of similitudes of $(V, ω)$ . When the space…

math.RT2018

Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials

Siddhartha Sahi, Jasper V. Stokman, Vidya Venkateswaran

Chinta and Gunnells introduced a rather intricate multi-parameter Weyl group action on rational functions on a torus, which, when the parameters are specialized to certain Gauss su…

math.RT2018

Generalized and degenerate Whittaker quotients and Fourier coefficients

Dmitry Gourevitch, Siddhartha Sahi

The study of Whittaker models for representations of reductive groups over local and global fields has become a central tool in representation theory and the theory of automorphic…

math.RT2018★ 4 cited

The Capelli eigenvalue problem for Lie superalgebras

Siddhartha Sahi, Hadi Salmasian, Vera Serganova

For a finite dimensional unital complex simple Jordan superalgebra $J$ , the Tits-Kantor-Koecher construction yields a 3-graded Lie superalgebra $\mathfrak g_\flat\cong \mathfrak g_…

math.RT2017

Schur $Q$ -functions and the Capelli eigenvalue problem for the Lie superalgebra $q (n)$

Alexander Alldridge, Siddhartha Sahi, Hadi Salmasian

Let $l := q (n) \times q (n)$ , where $q (n)$ denotes the queer Lie superalgebra. The associative superalgebra $V$ of type $Q (n)$ has a left and ri…

math.RT2016

Whittaker supports for representations of reductive groups

Raul Gomez, Dmitry Gourevitch, Siddhartha Sahi

Let $F$ be either $R$ or a finite extension of $Q_{p}$ , and let $G$ be a finite central extension of the group of $F$ -points of a reductive group defined over $F$ .…

math.RT2016

Quadratic Capelli operators and Okounkov polynomials

Siddhartha Sahi, Hadi Salmasian

Let $Z$ be the symmetric cone of $r \times r$ positive definite Hermitian matrices over a real division algebra $F$ . Then $Z$ admits a natural family of invariant different…

math.RT2016

Analytic continuation of equivariant distributions

Dmitry Gourevitch, Siddhartha Sahi, Eitan Sayag

We establish a method for constructing equivariant distributions on smooth real algebraic varieties from equivariant distributions on Zariski open subsets. This is based on Bernste…

math.RT2016★ 3 cited

Positivity of Shimura operators

Siddhartha Sahi, Genkai Zhang

In [16] G. Shimura introduced a family of invariant differential operators that play a key role in the study of nearly holomorphic automorphic forms, and he asked for a determinati…

math.RT2015

The Capelli identity and Radon transform for Grassmannians

Siddhartha Sahi, Genkai Zhang

We study a family $C_{s, l}$ of Capelli-type invariant differential operators on the space of rectangular matrices over a real division algebra. The $C_{s, l}$ descend to invariant d…

math.RT2015★ 1 cited

The Capelli problem for $gl (m ∣ n)$ and the spectrum of invariant differential operators

Siddhartha Sahi, Hadi Salmasian

The "Capelli problem" for the symmetric pairs $(gl \times gl, gl)$ $(gl, o)$ , and $(gl, sp)$ is closely rel…

math.RT2015★ 33 cited

Generalized and degenerate Whittaker models

Raul Gomez, Dmitry Gourevitch, Siddhartha Sahi

We study generalized and degenerate Whittaker models for reductive groups over local fields of characteristic zero (archimedean or non-archimedean). Our main result is the construc…

math.RT2014★ 6 cited

Invariant Functionals on the Speh representation

Dmitry Gourevitch, Siddhartha Sahi, Eitan Sayag

We study Sp(2n,R)-invariant functionals on the spaces of smooth vectors in Speh representations of GL(2n,R). For even n we give expressions for such invariant functionals using an…

math.RT2013★ 3 cited

Intertwining operators between line bundles on Grassmannians

Dmitry Gourevitch, Siddhartha Sahi

Let G=GL(n,F) where F is a local field of arbitrary characteristic, and let $π_{1}, π_{2}$ be representations induced from characters of two maximal parabolic subgroups $P_{1}, P_{2}$ . We ex…

math.RT2012★ 21 cited

Twisted homology for the mirabolic nilradical

Avraham Aizenbud, Dmitry Gourevitch, Siddhartha Sahi

The notion of derivatives for smooth representations of $G L (n, Q_{p})$ was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irr…

math.RT2012★ 10 cited

Degenerate Whittaker functionals for real reductive groups

Dmitry Gourevitch, Siddhartha Sahi

In this paper we establish a connection between the associated variety of a representation and the existence of certain degenerate Whittaker functionals, for both smooth and K-fini…

math.RT2011★ 19 cited

Derivatives for smooth representations of GL(n,R) and GL(n,C)

Avraham Aizenbud, Dmitry Gourevitch, Siddhartha Sahi

The notion of derivatives for smooth representations of GL(n) in the p-adic case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an analog of the highest de…

The Harish-Chandra isomorphism for supersymmetric spaces and ghost distributions

Classification of irreducible real modules of real Lie superalgebras

Restriction Theorems and Root Systems for Symmetric Superspaces

Eigenvalues of supersymmetric Shimura operators and interpolation polynomials

Quasi-polynomial representations of double affine Hecke algebras

A Stone-von Neumann equivalence of categories for smooth representations of the Heisenberg group

From Cauchy's determinant formula to bosonic and fermionic immanant identities

Capelli operators for spherical superharmonics and the Dougall-Ramanujan identity

Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials

Generalized and degenerate Whittaker quotients and Fourier coefficients

The Capelli eigenvalue problem for Lie superalgebras

Schur Q-functions and the Capelli eigenvalue problem for the Lie superalgebra q(n)

Whittaker supports for representations of reductive groups

Quadratic Capelli operators and Okounkov polynomials

Analytic continuation of equivariant distributions

Positivity of Shimura operators

The Capelli identity and Radon transform for Grassmannians

The Capelli problem for gl(m∣n) and the spectrum of invariant differential operators

Generalized and degenerate Whittaker models

Invariant Functionals on the Speh representation

Intertwining operators between line bundles on Grassmannians

Twisted homology for the mirabolic nilradical

Degenerate Whittaker functionals for real reductive groups

Derivatives for smooth representations of GL(n,R) and GL(n,C)

Schur $Q$ -functions and the Capelli eigenvalue problem for the Lie superalgebra $q (n)$

The Capelli problem for $gl (m ∣ n)$ and the spectrum of invariant differential operators