Toshiyuki Kobayashi

activity

20012023

most citedExperimental demonstration of the time reversal Aharonov-Casher effect

175 citations · 1.5k across the 67 of their papers we have counts for

collaborators

70 papers

math.CV2023

A generating operator for Rankin-Cohen brackets

Toshiyuki Kobayashi, Michael Pevzner

Motivated by the classical ideas of generating functions for orthogonal polynomials, we initiate a new line of investigation on "generating operators" for a family of differential…

math.RT2022★ 1 cited

Bounded multiplicity branching for symmetric pairs

Toshiyuki Kobayashi

We prove that any simply connected non-compact semisimple Lie group $G$ admits an infinite-dimensional irreducible representation $Π$ with bounded multiplicity property of the rest…

math.RT2022★ 5 cited

Conjectures on reductive homogeneous spaces

Toshiyuki Kobayashi

We address some conjectures and open problems in "analysis of symmetries" which include the study of non-commutative harmonic analysis and discontinuous groups for reductive homoge…

math.RT2022★ 3 cited

Multiplicity in restricting minimal representations

Toshiyuki Kobayashi

We discuss the action of a subgroup on small nilpotent orbits, and prove a bounded multiplicity property for the restriction of minimal representations of real reductive Lie groups…

math.RT2021

Recent advances in branching problems of representations

Toshiyuki Kobayashi

How does an irreducible representation of a group behave when restricted to a subgroup? This is part of branching problems, which are one of the fundamental problems in representat…

math.RT2021★ 3 cited

Bounded multiplicity theorems for induction and restriction

Toshiyuki Kobayashi

We prove a geometric criterion for the bounded multiplicity property of "small" infinite-dimensional representations of real reductive Lie groupsin both induction and restrictions.…

math.RT2021

Temperedness criterion of the tensor product of parabolic induction for $G L_{n}$

Yves Benoist, Yui Inoue, Toshiyuki Kobayashi

We give a necessary and sufficient condition for a pair of parabolic subgroups $P$ and $Q$ of $G = G L_{n} (R)$ such that the tensor product of any two unitarily induced represe…

math.GR2020★ 6 cited

Tempered homogeneous spaces III

Yves Benoist, Toshiyuki Kobayashi

Let G be a real semisimple algebraic Lie group and H a real reductive algebraic subgroup. We describe the pairs (G,H) for which the representation of G in $L^{2} (G / H)$ is tempered. W…

math.GR2020★ 1 cited

Tempered homogeneous spaces IV

Yves Benoist, Toshiyuki Kobayashi

Let G be a complex semisimple Lie group and H a complex closed connected subgroup. Let g and h be their Lie algebras. We prove that the regular representation of G in $L^{2} (G / H)$ is…

math.RT2020

Topics on global analysis of manifolds and representation theory of reductive groups

Toshiyuki Kobayashi

Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments o…

math.RT2020★ 1 cited

A hidden symmetry of a branching law

Toshiyuki Kobayashi, Birgit Speh

We consider branching laws for the restriction of some irreducible unitary representations $Π$ of $G = O (p, q)$ to its subgroup $H = O (p - 1, q)$ . In Kobayashi (arXiv:1907.07994), the irre…

math.SP2020★ 6 cited

Spectral analysis on pseudo-Riemannian locally symmetric spaces

Fanny Kassel, Toshiyuki Kobayashi

We summarize recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $Γ\ G / H$ , beyond the classical setting where $H$ is compact (e.g. th…

math.RT2019★ 2 cited

Spectral analysis on standard locally homogeneous spaces

Fanny Kassel, Toshiyuki Kobayashi

Let $X = G / H$ be a reductive homogeneous space with $H$ noncompact, endowed with a $G$ -invariant pseudo-Riemannian structure. Let $L$ be a reductive subgroup of $G$ acting properly o…

math.RT2019★ 7 cited

Admissible restrictions of irreducible representations of reductive Lie groups: symplectic geometry and discrete decomposability

Toshiyuki Kobayashi

Let $G$ be a real reductive Lie group, $L$ a compact subgroup, and $π$ an irreducible admissible representation of $G$ . In this article we prove a necessary and sufficient conditio…

math.RT2019★ 17 cited

Branching laws of unitary representations associated to minimal elliptic orbits for indefinite orthogonal group O(p,q)

Toshiyuki Kobayashi

We give a complete description of the discrete spectra in the branching law $Π ∣_{G^{'}}$ with respect to the pair $(G, G^{'}) = (O (p, q), O (p^{'}, q^{'}) \times O (p^{''}, q^{''}))$ for irreducible unitary…

math.RT2019

Distinguished representations of SO(n+1,1) x SO(n,1), periods and branching laws

Toshiyuki Kobayashi, Birgit Speh

Given irreducible representations $Π$ and $π$ of the rank one special orthogonal groups $G = S O (n + 1, 1)$ and $G^{'} = S O (n, 1)$ with nonsingular integral infinitesimal character, we state i…

math.RT2018★ 2 cited

Inversion of Rankin-Cohen operators via Holographic Transform

Toshiyuki Kobayashi, Michael Pevzner

The analysis of branching problems for restriction of representations brings the concept of symmetry breaking transform and holographic transform. Symmetry breaking operators decre…

math.RT2018★ 4 cited

Invariant differential operators on spherical homogeneous spaces with overgroups

Fanny Kassel, Toshiyuki Kobayashi

We investigate the structure of the ring $D_{G} (X)$ of $G$ -invariant differential operators on a reductive spherical homogeneous space $X = G / H$ with an overgroup $\widetilde…

math.RT2018★ 9 cited

Geometry of coadjoint orbits and multiplicity-one branching laws for symmetric pairs

Toshiyuki Kobayashi, Salma Nasrin

Consider the restriction of an irreducible unitary representation $π$ of a Lie group $G$ to its subgroup $H$ . Kirillov's revolutionary idea on the orbit method suggests that the mu…

math.RT2018★ 45 cited

Symmetry breaking for representations of rank one orthogonal groups II

Toshiyuki Kobayashi, Birgit Speh

For a pair $(G, G^{'}) = (O (n + 1, 1), O (n, 1))$ of reductive groups, we investigate intertwining operators (symmetry breaking operators) between principal series representations $I_{δ} (V, λ)$ …

math.RT2017★ 1 cited

Conformal symmetry breaking on differential forms and some applications

Toshiyuki Kobayashi

Rapid progress has been made recently on symmetry breaking operators for real reductive groups. Based on Program A-C for branching problems (T.Kobayashi [Progr.Math.2015]), we illu…

math.RT2017★ 8 cited

Residue formula for regular symmetry breaking operators

Toshiyuki Kobayashi

We prove an explicit residue formula for a meromorphic continuation of conformally covariant integral operators between differential forms on $R^{n}$ and on its hyperplane. The…

math.RT2017★ 11 cited

Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad

Toshiyuki Kobayashi, Birgit Speh

We consider irreducible unitary representations $A_{i}$ of G=SO(n+1,1) with the same infinitesimal character as the trivial representation and representations $B_{j}$ of H=SO(n,1) with…

math.DG2016★ 2 cited

Conformal symmetry breaking operators for anti-de Sitter spaces

Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner

For a pseudo-Riemannian manifold $X$ and a totally geodesic hypersurface $Y$ , we consider the problem of constructing and classifying all linear differential operators $\mathcal{E}…

A generating operator for Rankin-Cohen brackets

Bounded multiplicity branching for symmetric pairs

Conjectures on reductive homogeneous spaces

Multiplicity in restricting minimal representations

Recent advances in branching problems of representations

Bounded multiplicity theorems for induction and restriction

Temperedness criterion of the tensor product of parabolic induction for GLn​

Tempered homogeneous spaces III

Tempered homogeneous spaces IV

Topics on global analysis of manifolds and representation theory of reductive groups

A hidden symmetry of a branching law

Spectral analysis on pseudo-Riemannian locally symmetric spaces

Spectral analysis on standard locally homogeneous spaces

Admissible restrictions of irreducible representations of reductive Lie groups: symplectic geometry and discrete decomposability

Branching laws of unitary representations associated to minimal elliptic orbits for indefinite orthogonal group O(p,q)

Distinguished representations of SO(n+1,1) x SO(n,1), periods and branching laws

Inversion of Rankin-Cohen operators via Holographic Transform

Invariant differential operators on spherical homogeneous spaces with overgroups

Geometry of coadjoint orbits and multiplicity-one branching laws for symmetric pairs

Symmetry breaking for representations of rank one orthogonal groups II

Conformal symmetry breaking on differential forms and some applications

Residue formula for regular symmetry breaking operators

Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad

Conformal symmetry breaking operators for anti-de Sitter spaces

Temperedness criterion of the tensor product of parabolic induction for $G L_{n}$