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Almost Kähler geometry of adjoint orbits of semisimple Lie groups
We study the almost Kähler geometry of adjoint orbits of non-compact real semisimple Lie groups endowed with the Kirillov–Kostant–Souriau symplectic...
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The Katzarkov–Kontsevich–Pantev conjecture for minimal adjoint orbits
We consider minimal semisimple adjoint orbits as Landau–Ginzburg models and prove that they satisfy the conjecture of Katzarkov–Kontsevich–Pantev...
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The Enhanced Period Map and Equivariant Deformation Quantizations of Nilpotent Orbits
In a previous paper, the author and his collaborator studied the problem of lifting Hamiltonian group actions on symplectic varieties and Lagrangian...
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On the Semisimple Orbits of Restricted Cartan Type Lie Algebras W, S and H
In this short note, we give a description of semisimple orbits in the restricted Cartan type Lie algebras W , S , H .
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Compatibility of semisimple local Langlands parameters with parahoric Satake parameters
In this paper, we prove that there is at most one correspondence between parahoric-spherical representations and semisimple local Langlands...
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Deformations of symplectic singularities and orbit method for semisimple Lie algebras
We classify filtered quantizations of conical symplectic singularities and use this to show that all filtered quantizations of symplectic quotient...
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Superpotentials and Quiver Algebras for Semisimple Hopf Actions
We consider the action of a semisimple Hopf algebra H on an m -Koszul Artin–Schelter regular algebra A . Such an algebra A is a derivation-quotient...
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Translates of S-arithmetic periodic orbits and applications
We prove that certain sequences of periodic orbits of the diagonal group in the space of lattices equidistribute. As an application we obtain new...
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On the parametrization of nilpotent orbits
The aim of this article is to give a detailed proof of the standard well-known results regarding parametrization of the nilpotent orbits in simple...
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Modular Tensor Categories, Subcategories, and Galois Orbits
We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes...
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Benjamini-Schramm convergence of periodic orbits
We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous...
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On the regular representation of solvable Lie groups with open coadjoint quasi-orbits
We obtain a Lie theoretic intrinsic characterization of the connected and simply connected solvable Lie groups whose regular representation is a...
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A survey of semisimple algebras in algebraic combinatorics
This is a survey of semisimple algebras of current interest in algebraic combinatorics, with a focus on questions which we feel will be new and...
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GALOIS COHOMOLOGY OF REAL SEMISIMPLE GROUPS VIA KAC LABELINGS
For a connected semisimple group G over the field of real numbers ℝ, using a method of Onishchik and Vinberg, we compute the first Galois cohomology...
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The Radon transform for double fibrations of semisimple symmetric spaces
We present the injectivity and support results of the Radon transform for the double fibrations of semisimple symmetric spaces in the setting of the...
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Geometric Structures on the Orbits of Loop Diffeomorphism Groups and Related Heavenly-Type Hamiltonian Systems. I
We present a review of differential-geometric and Lie-algebraic approaches to the investigation of a broad class of nonlinear integrable differential...
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Homogeneous Sub-Riemannian Manifolds Whose Normal Extremals are Orbits
In this paper, we study homogeneous sub-Riemannian manifolds whose normal extremals are the orbits of one-parameter subgroups of the group of smooth...
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SEMISIMPLE CYCLIC ELEMENTS IN SEMISIMPLE LIE ALGEBRAS
This paper is a continuation of the theory of cyclic elements in semisimple Lie algebras, developed by Elashvili, Kac and Vinberg. Its main result is...