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Iwahori-Spherical Representations
Let F be a nonarchimedean local field of characteristic zero, and let...
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A classification of spherical Schubert varieties in the Grassmannian
Let L be any standard Levi subgroup which acts by left multiplication on a Schubert variety X ( w ) in the Grassmannian. We give a complete...
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Kohn–Rossi cohomology of spherical CR manifolds
We prove some vanishing theorems for the Kohn–Rossi cohomology of some spherical CR manifolds. To this end, we use a canonical contact form defined...
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Spherical Harmonics
Spherical harmonics play an important role in electrodynamics and in quantum mechanics. We shall show how they appear in the representation theory of...
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Gelfand pairs and spherical means on H-type groups
We study the injectivity of the spherical mean operator associated to the Gelfand pairs ( U , N ), where N is a Heisenberg type group and U the subgroup...
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Fan Valuations and Spherical Intrinsic Volumes
We generalize valuations on polyhedral cones to valuations on (plane) fans. For fans induced by hyperplane arrangements, we show a correspondence...
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Arithmetic fundamental lemma for the spherical Hecke algebra
We define Hecke correspondences and Hecke operators on unitary RZ spaces and study their basic geometric properties, including a commutativity...
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Families of canonical local periods on spherical varieties
We consider the variation of canonical local periods on spherical varieties proposed by Sakellaridis–Venkatesh in families. We formulate conjectures...
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Spherical Schubert varieties and pattern avoidance
A normal variety X is called H - spherical for the action of the complex reductive group H if it contains a dense orbit of some Borel subgroup of H . We...
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Spherical tropicalization and Berkovich analytification
Let X be a spherical variety. We show that Tevelev and Vogiannou’s tropicalization map from X to its tropicalization factors through the Berkovich...
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Bounded spherical functions and Heisenberg inequality on quaternionic Heisenberg group
In this paper, we will construct the bounded spherical functions of the quaternionic Heisenberg group using the theory of representations of the...
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Spherical objects and stability conditions on 2-Calabi–Yau quiver categories
We study actions of spherical twists on 2-Calabi–Yau categories with a Bridgeland stability condition. In these categories, we describe how to reduce...
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Equivariant Cobordism of Smooth Projective Spherical Varieties
We study the equivariant cobordism rings for the action of a torus T on smooth varieties over an algebraically closed field of characteristic zero....
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The Manin–Peyre conjecture for smooth spherical Fano threefolds
The Manin–Peyre conjecture is established for smooth spherical Fano threefolds of semisimple rank one and type N . Together with the previously solved...
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Angular Distance: Spherical and Hyperbolic Geometry
The geometry of the sphere is familiar to us, from everyday life as well as from geography. It is a part of the metric geometry of space, yet it...