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Multiplicity in Restricting Minimal Representations
We discuss the action of a subgroup on small nilpotent orbits, and prove a bounded multiplicity property for the restriction of minimal...
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On parabolic subgroups of Artin groups
Given an Artin group A Γ , a common strategy in the study of A Γ is the reduction to parabolic subgroups whose defining graphs have small diameter,...
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On the Action of the Restricted Weyl Group on the Set of Orbits a Minimal Parabolic Subgroup
AbstractWe construct the action of the restricted Weyl group on the set of principal families of orbits of a minimal parabolic subgroup over an...
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Proper elements of Coxeter groups
We extend the notion of proper elements to all finite Coxeter groups. For all infinite families of finite Coxeter groups we prove that the...
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4d Theories, Fivebranes, and M-Theory
In this section, we study line operators in the 4d \(\mathcal {N}=2^*\)...
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Analytic Properties of Spherical Cusp Forms on GL(n)
Let φ be an L 2 -normalized spherical vector in an everywhere unramified cuspidal automorphic representation of PGL n over ℚ with Laplace eigenvalue λ φ ....
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Strong Transitivity, the Moufang Condition and the Howe–Moore Property
Firstly, we prove that every closed subgroup H of type-preserving automorphisms of a locally finite thick affine building Δ of dimension ≥ 2 that...
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2d Sigma-Models and DAHA
In this section, we study representation theory of DAHA, strictly speaking, the spherical subalgebra of DAHA of type...
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Spherical Harmonics and Linear Representations of Lie Groups
This chapter and the next focus on topics that are somewhat different from the more geometric and algebraic topics discussed in the previous...
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Lie hyperalgebras
We define the Lie hyperalgebra of a Lie hypergroup as the smallest (possibly infinite dimensional) Lie algebra containing left invariant vector...
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EQUIVARIANT MODELS OF SPHERICAL VARIETIES
Let G be a connected semisimple group over an algebraically closed field k of characteristic 0. Let Y = G / H be a spherical homogeneous space of G ,...
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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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GRÖBNER THEORY AND TROPICAL GEOMETRY ON SPHERICAL VARIETIES
Let G be a connected reductive algebraic group. We develop a Gröbner theory for multiplicity-free G -algebras, as well as a tropical geometry for...
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Coxeter Groups, Artin Groups, Buildings
The basic notion in this chapter is a Coxeter system...
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The Exceptional Tits Quadrangles Revisited
Tits polygons are generalizations of Moufang polygons in which the neighborhood of each vertex is endowed with an “opposition relation.” There is a...