175 citations · 1.5k across the 67 of their papers we have counts for
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Bounded multiplicity branching for symmetric pairs
Toshiyuki Kobayashi
We prove that any simply connected non-compact semisimple Lie group admits an infinite-dimensional irreducible representation with bounded multiplicity property of the rest…
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…
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…
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…
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.…
Temperedness criterion of the tensor product of parabolic induction for
Yves Benoist, Yui Inoue, Toshiyuki Kobayashi
We give a necessary and sufficient condition for a pair of parabolic subgroups and of such that the tensor product of any two unitarily induced represe…
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…
A hidden symmetry of a branching law
Toshiyuki Kobayashi, Birgit Speh
We consider branching laws for the restriction of some irreducible unitary representations of to its subgroup . In Kobayashi (arXiv:1907.07994), the irre…
Spectral analysis on standard locally homogeneous spaces
Fanny Kassel, Toshiyuki Kobayashi
Let be a reductive homogeneous space with noncompact, endowed with a -invariant pseudo-Riemannian structure. Let be a reductive subgroup of acting properly o…
Admissible restrictions of irreducible representations of reductive Lie groups: symplectic geometry and discrete decomposability
Toshiyuki Kobayashi
Let be a real reductive Lie group, a compact subgroup, and an irreducible admissible representation of . In this article we prove a necessary and sufficient conditio…
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 with respect to the pair for irreducible unitary…
Distinguished representations of SO(n+1,1) x SO(n,1), periods and branching laws
Toshiyuki Kobayashi, Birgit Speh
Given irreducible representations and of the rank one special orthogonal groups and with nonsingular integral infinitesimal character, we state i…
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…
Invariant differential operators on spherical homogeneous spaces with overgroups
Fanny Kassel, Toshiyuki Kobayashi
We investigate the structure of the ring of -invariant differential operators on a reductive spherical homogeneous space with an overgroup $\widetilde…
Geometry of coadjoint orbits and multiplicity-one branching laws for symmetric pairs
Toshiyuki Kobayashi, Salma Nasrin
Consider the restriction of an irreducible unitary representation of a Lie group to its subgroup . Kirillov's revolutionary idea on the orbit method suggests that the mu…
Symmetry breaking for representations of rank one orthogonal groups II
Toshiyuki Kobayashi, Birgit Speh
For a pair of reductive groups, we investigate intertwining operators (symmetry breaking operators) between principal series representations …
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…
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 and on its hyperplane. The…
Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad
Toshiyuki Kobayashi, Birgit Speh
We consider irreducible unitary representations of G=SO(n+1,1) with the same infinitesimal character as the trivial representation and representations of H=SO(n,1) with…
Global analysis by hidden symmetry
Toshiyuki Kobayashi
Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship betwee…
A program for branching problems in the representation theory of real reductive groups
Toshiyuki Kobayashi
We wish to understand how irreducible representations of a group G behave when restricted to a subgroup G' (the branching problem). Our primary concern is with representations of r…
Global uniqueness of small representations
Toshiyuki Kobayashi, Gordan Savin
We prove that automorphic representations whose local components are certain small representations have multiplicity one. The proof is based on the multiplicity-one theorem for cer…
Vector-valued covariant differential operators for the Möbius transformation
Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner
We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential oper…
Shintani functions, real spherical manifolds, and symmetry breaking operators
Toshiyuki Kobayashi
For a pair of reductive groups , we prove a geometric criterion for the space of Shintani functions to be finite-dimensional in the Archimedean case. This…