Zobrazeno 1 - 10
of 1 474
pro vyhledávání: '"22E45"'
We develop a novel perspective on reflection positivity (RP) on the strip by systematically developing the analogies with the unit disc and the upper half plane in the complex plane. These domains correspond to the three conjugacy classes of one-para
Externí odkaz:
http://arxiv.org/abs/2407.21123
Autor:
Okuda, Takayuki
For a non-compact simple Lie algebra $\mathfrak{g}$ over $\mathbb{R}$, we denote by $\mathcal{O}^{\mathbb{C}}_{\min,\mathfrak{g}}$ the unique complex nilpotent orbit in $\mathfrak{g} \otimes_\mathbb{R} \mathbb{C}$ containing all minimal real nilpoten
Externí odkaz:
http://arxiv.org/abs/2407.00675
We realize all irreducible unitary representations of the group $\mathrm{SO}_0(n+1,1)$ on explicit Hilbert spaces of vector-valued $L^2$-functions on $\mathbb{R}^n\setminus\{0\}$. The key ingredient in our construction is an explicit expression for t
Externí odkaz:
http://arxiv.org/abs/2406.11349
In this paper, we study Toeplitz operators on generalized flag manifolds of compact Lie groups using a representation-theoretic point of view. We prove several basic properties of these Toeplitz operators, including an abstract formula for their matr
Externí odkaz:
http://arxiv.org/abs/2406.10804
Autor:
Nakahama, Ryosuke
Let $(G,G_1)$ be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces $D_1=G_1/K_1\subset D=G/K$, realized as bounded symmetric domains in complex vector spaces $\mathfrak{p}^+_1\subset\mathfrak{p}^+$ respectivel
Externí odkaz:
http://arxiv.org/abs/2406.01905
Let $(\tau, V_{\tau})$ be a finite dimensional representation of a maximal compact subgroup $K$ of a connected non-compact semisimple Lie group $G$, and let $\Gamma$ be a uniform torsion-free lattice in $G$. We obtain an infinitesimal version of the
Externí odkaz:
http://arxiv.org/abs/2405.09847
Autor:
Ditlevsen, Jonathan, Frahm, Jan
The pair of real reductive groups $(G,H)=(\operatorname{GL}(n+1,\mathbb{R}),\operatorname{GL}(n,\mathbb{R}))$ is a strong Gelfand pair, i.e. the multiplicities $\dim\operatorname{Hom}_H(\pi|_H,\tau)$ are either $0$ or $1$ for all irreducible Casselma
Externí odkaz:
http://arxiv.org/abs/2403.14267
Autor:
Simon, Tobias
In this paper, we provide a simpler proof of the Kr\"otz--Stanton Extension Theorem for holomorphic extensions of orbit maps in unitary irreducible representations of connected semisimple Lie groups. Our result is a generalization of the previous res
Externí odkaz:
http://arxiv.org/abs/2403.13572
Autor:
Kuhn, Maria Gabriella
Let $G=PGL(2,Q_q)$. In this paper we shall investigate the group of measurable currents taking values in $G$. The key observation is that $G$ is acting by automorphisms on a homogeneous tree, which will play the role of the upper half plane in the ca
Externí odkaz:
http://arxiv.org/abs/2403.12956
Autor:
Barchini, Leticia, Trapa, Peter E.
Fix an integral semisimple element $\lambda$ in the Lie algebra $\mathfrak{g}$ of a complex reductive algebraic group $G$. Let $L$ denote the centralizer of $\lambda$ in $G$ and let $\mathfrak{g}(-1)$ denote the $-1$ eigenspace of $\mathrm{ad}(\lambd
Externí odkaz:
http://arxiv.org/abs/2402.17956