arXiv subjects

Tobias Pecher

Publications and source records attributed to Tobias Pecher.

4 recordsLinked to original sources

arXiv2018

Classification of reductive real spherical pairs II. The semisimple case

If ${\mathfrak g}$ is a real reductive Lie algebra and ${\mathfrak h} < {\mathfrak g}$ is a subalgebra, then $({\mathfrak g}, {\mathfrak h})$ is called real spherical provided that ${\mathfrak g} = {\mathfrak h} + {\mathfrak p}$ for some choice of a minimal parabolic subalgebra ${\mathfrak p} \subset {\mathfrak g}$. In this paper we classify all real spherical pairs $({\mathfrak g}, {\mathfrak h})$ where ${\mathfrak g}$ is semi-simple but not simple and ${\mathfrak h}$ is a reductive real algebraic subalgebra. The paper is based on the classification of the case where ${\mathfrak g}$ is simple (see arXiv:1609.00963) and generalizes the results of Brion and Mikityuk in the (complex) spherical case.

math.RT↗

arXiv2018

Classification of reductive real spherical pairs I. The simple case

This paper gives a classification of all pairs $(\mathfrak g, \mathfrak h)$ with $\mathfrak g$ a simple real Lie algebra and $\mathfrak h < \mathfrak g$ a reductive subalgebra for which there exists a minimal parabolic subalgebra $\mathfrak p < \mathfrak g$ such that $\mathfrak g = \mathfrak h + \mathfrak p$ as vector sum.

math.RT↗

arXiv2011

Classification of skew multiplicity free modules

Let $G$ be a connected reductive group defined over $\CC$ with a finite dimensional representation $V$. The action of $G$ is said to be skew multiplicity-free (SMF) if the exterior algebra $\bigwedge V$ contains no irreducible representation of $G$ with multiplicity $> 1$. In this paper we classify all such representations.

math.RT↗

arXiv2011

Multiplicity-free super vector spaces

Let $V$ be a complex finite dimensional super vector space with an action of a connected semisimple group $G$. We classify those pairs $(G,V)$ for which all homogeneous components of the super symmetric algebra of $V$ decompose multiplicity-free.

math.RT↗