Related papers: A new proof of Harish-Chandra's integral formula

Consider a Hamiltonian action of a compact Lie group H on a compact symplectic manifold (M,w) and let G be a subgroup of the diffeomorphism group Diff(M). We develop techniques to decide when the maps on rational homotopy and rational…

For a finite-dimensional Lie algebra $\mathfrak{L}$ over $\mathbb{C}$ with a fixed Levi decomposition $\mathfrak{L} = \mathfrak{g} \oplus \mathfrak{r}$ where $\mathfrak{g}$ is semi-simple, we investigate $\mathfrak{L}$-modules which…

The purpose of this article is to give the first complete proof of the Whittaker Plancherel Theorem. The proof uses Harish-Chandra's Plancherel Theorem for a real reductive group and its exposition can be used as an introduction to…

Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade one regular semisimple elements from non-equivalent Heisenberg subalgebras of a loop algebra $\G\otimes{\bf C}[\lambda,\lambda^{-1}]$ are studied. The graded…

As a generalization to the heat semigroup on the Heisenberg group, the diffusion semigroup generated by the subelliptic operator $L:=\ff 1 2 \sum_{i=1}^m X_i^2$ on $\R^{m+d}:= \R^m\times\R^d$ is investigated, where $$X_i(x,y)= \sum_{k=1}^m…

This work consist of two interrelated parts. First, we derive massive gauge-invariant generalizations of geometric actions on coadjoint orbits of arbitrary (infinite-dimensional) groups $G$ with central extensions, with gauge group $H$…

We prove three new results about the global Springer action defined in \cite{GSI}. The first one determines the support of the perverse cohomology sheaves of the parabolic Hitchin complex, which serves as a technical tool for the next…

We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let $N$ be a connected, simply connected nilpotent Lie group with a dilation structure (a homogeneous group) and let $(\pi,…

We show that for any finite connected reductive group, a Jordan decomposition can always be chosen such that it commutes with Harish-Chandra induction. En route, we show that the endomorphism algebra of the Harish-Chandra induction of a…

Let G be complex linear-algebraic group, H a subgroup, which is dense in G in the Zariski-topology. Assume that G/[G,G] is reductive and furthermore that (1) G is solvable, or (2) the semisimple elements in G'=[G,G] are dense. Then every…

Let $G$ be a real reductive linear group in the Harish-Chandra class. Suppose that $P$ is a parabolic subgroup of $G$ with Langlands decomposition $P=MAN$. Let $\pi$ be an irreducible representation of the Levi factor $L=MA$. We give…

We continue the study of Harish-Chandra bimodules in the setting of the Deligne categories $\mathrm{Rep}(G_t)$, that was started in the previous work of the first author (arXiv:2002.01555). In this work we construct a family of…

Let $G$ be a countable group. We introduce several equivalence relations on the set ${\rm Sub}(G)$ of subgroups of $G$, defined by properties of the quasi-regular representations $\lambda_{G/H}$ associated to $H\in {\rm Sub}(G)$ and compare…

We observe that all classical Hamiltonian systems coming from the invariant polynomials on a reductive Lie algebra g can be integrated in a universal way. This is a consequence of Ng\^o's action of the group scheme J of regular centralizers…

In this paper we use the heat equation in a group of Heisenberg type $\mathbb{G}$ to provide a unified treatment of the two very different extension problems for the time independent pseudo-differential operators $\mathscr L^s$ and…

Ozsvath and Szabo construct a spectral sequence with E_2 term \Lambda^*(H^1(Y;Z))\otimes Z[U,U^{-1}] converging to HF^\infty(Y,s) for a torsion Spin^c structure s. They conjecture that the differentials are completely determined by the…

Understanding the thermalization process in a pure quantum system is a challenge in theoretical physics. In this work, we explore possible thermalization mechanism in Yang-Mills(YM) theory by using a positive semi-definite quantum…

The two papers in this series analyze quantum invariant differential operators for quantum symmetric spaces in the maximally split case. In this paper, we complete the proof of a quantum version of Harish-Chandra's theorem: There is a…

An oscillator group $G$ is a semidirect product of a Heisenberg group with a one-parameter group. In this article we construct Olshanski semigroups for infinite-dimensional oscillator groups. These are complex involutive semigroups which…

Given a supercuspidal representation $\sigma$ of a parabolic subgroup $P$ of reductive group $G$, we discover a universal hierarchical structure of reducibility of the parabolic induction $Ind^G_P(\sigma)$, i.e. always irreducible from some…