Related papers: Multiplicity in restricting minimal representation…

We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…

Let $G$ be a simply connected algebraic group of type $B,C$ or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the dual vector space of the Lie algebra of $G$. In particular, we…

The unipotent groups are an important class of algebraic groups. We show that techniques used to compute with finitely generated nilpotent groups carry over to unipotent groups. We concentrate particularly on the maximal unipotent subgroup…

We compute the number of orbit types for simply connected simple algebraic groups over algebraically closed fields as well as for compact simply connected simple Lie groups. We also compute the number of orbit types for the adjoint action…

The purpose of this article is to describe and characterize the limit distributions of translates of a bounded open "piece of orbit" of a reductive subgroup on a space of S-arithmetic lattices. This is accomplished under a mild assumption…

We reduce the local limit theorem for a non-compact semisimple Lie group acting on its symmetric space to establishing that a natural operator associated to the measure is quasicompact. Under strong Diophantine assumptions on the underlying…

We give a necessary and sufficient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biharmonic in terms of symmetric triad with multiplicities. By…

In the paper "The Second cohomology of nilpotent orbits in classical Lie algebras, Kyoto J. Math. 60 (2020), no. 2, 717-799" by I. Biswas, P. Chatterjee and C. Maity homotopy types of nilpotent orbits are explicitly described in the case of…

We obtain inductive and enumerative formulas for the multiplicities of the weights of the spin module for the Clifford algebra of a Levi subalgebra in a complex semisimple Lie algebra. Our formulas involve only matrices and tableaux, and…

We describe algorithms for computing the induced nilpotent orbits in semisimple Lie algebras. We use them to obtain the induction tables for the Lie algebras of exceptional type. This also yields the classification of the rigid nilpotent…

We study a shift action defined on multipartitions and on residue multisets of their Young diagrams. We prove that the minimal orbit cardinality among all multipartitions associated to a given multiset depends only on the orbit cardinality…

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

We find the explicit branching laws for the restriction of minimal holomorphic representations to symmetric subgroups in the case where the restriction is discretely decomposable. For holomorphic pairs the minimal holomorphic representation…

Let $G$ be a connected and simply connected two-step nilpotent Lie group and $\Gamma$ a lattice subgroup of $G$. In this note, we give a new multiplicity formula, according to the sense of Moore, of irreducible unitary representations…

We show that the maximal orbit dimension of a simultaneous Lie group action on n copies of a manifold does not pseudo-stabilize when n increases. We also show that if a Lie group action is (locally) effective on subsets of a manifold, then…

We prove the multiplicity one theorem for min-max free boundary minimal hypersurfaces in compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To approach this, we develop existence and regularity theory for free…

We show that irreducible unitary representations of nilpotent super Lie groups can be obtained by induction from a distinguished class of sub super Lie groups. These sub super Lie groups are natural analogues of polarizing subgroups that…

Motivated by geometric Langlands, we initiate a program to study the mirror symmetry between nilpotent orbit closures of a semisimple Lie algebra and those of its Langlands dual. The most interesting case is $B_n$ via $C_n$. Classically,…

We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence are imposed on certain components of the subgrading. This allows us to obtain some useful information about the…